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STEAM  ENGINE. 

STATIONARY — MARINE — LOCOMOTIVE — GAS  ENGINES,  ETC. 

THEORY  OP  STEAM  ENGINE. 

Translated  from  the  fourth  edition  of  Weisbach's  Mechanics, 
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INDICATOR  PRACTICE  AND  STEAM  ENGINE 
ECONOMY. 

Witti  Plain  Directions  for  Attaching  the  Indicator,  Taking 
Diagrams,  Computing  the  Horse-power,  Drawing  the  Theo- 
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"  Must  be  a  boon  to  the  every-day  engineer  who  is  seeking  informa- 
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PUBLISHED  AND  FOB  BALE  BY 


JOHN  WILEY  &  SONS,  Astor  Place,  New  York, 

*+*Will  be  mailed,  prepaid,  on  the  receipt  of  the  price. 


THERMODYNAMICS 


OF  THE 


STEAM-ENGINE 


AND    OTHER    HEAT-ENGINES. 


BY 


CECIL  H.  PEABODY, 

ASSOCIATE  PROFESSOR  OF  STEAM  ENGINEERING,  MASSACHUSETTS  INSTITUTE  OF  TECHNOLOGY. 


NEW    YORK: 
JOHN    WILEY    &    SONS, 

15  ASTOR   PLACE, 
1889. 


G> 


Copyright,  1889, 

BY 
CECIL   H.  PEABODY. 


DRUMMONT>  &  NEU,  FERRIS  BROS., 

Electrotype™,  Printers, 

1  to  7  Hague  Street,  826  Pearl  Street, 

New  York.  New  York. 


PREFACE. 


THIS  work  is  designed  to  give  instruction  to  students  in 
technical  schools  in  the  methods  and  results  of  the  application 
of  thermodynamics  to  engineering.  While  it  has  been  consid- 
ered desirable  to  follow  commonly  accepted  methods,  some  parts 
differ  from  other  text-books,  either  in  substance  or  in  manner 
of  presentation,  and  may  require  a  few  words  of  explanation. 

The  general  theory  or  formal  presentation  of  thermodynam- 
ics is  that  employed  by  the  majority  of  writers,  and  was  pre- 
pared with  the  view  of  present&g  clearly  the  difficulties  inher- 
ent in  the  subject,  and  of  giving  familiarity  with  the  processes 
employed. 

In  the  discussion  of  the  properties  of  gases  and  vapors  the 
original  experimental  data  on  which  the  working  equations, 
whether  logical  or  empirical,  must  be  based  are  given  quite 
fully,  to  afford  an  idea  of  the  degree  of  accuracy  attainable  in 
calculations  made  with  their  aid.  Rowland's  determination  of 
the  mechanical  equivalent  of  heat  has  been  adopted,  and  with 
it  his  determination  of  the  specific  heat  of  water  at  low  tem- 
peratures. The  author's  "  Tables  of  the  Properties  of  Satu- 
rated Steam  and  Other  Vapors  "  were  calculated  to  accompany 
this  work,  and  may  be  considered  to  be  an  integral  part  of  it. 

The  chapters  on  the  flow  of  gases  and  vapors  and  on  the  in- 
jector are  believed  to  present  some  novel  features,  especially 
in  the  comparisons  with  experiments. 

The  feature  in  which  this  book  differs  most  from  similar 
works  is  in  the  treatment  of  the  steam-engine.  It  has  been 
deemed  advisable  to  avoid  all  approximate  theories  based  on 
the  assumption  of  adiabatic  changes  of  steam  in  an  engine  cyl- 


IV  PREFACE. 

inder,  and  instead  to  make  a  systematic  study  of  steam-engine 
tests,  with  the  view  of  finding  what  is  actually  known  on  the 
subject,  and  how  future  investigations  and  improvements  may 
be  made.  For  this  purpose  a  large  number  of  tests  have  been 
collected,  arranged,  and  compared.  Special  attention  is  given 
to  the  investigations  of  the  action  of  steam  in  the  cylinder  of 
an  engine,  considerable  space  being  given  to  Hirn's  researches 
and  to  experiments  that  provide  the  basis  for  them.  Direc- 
tions are  given  for  testing  engines,  and  for  designing  simple 
and  compound  engines. 

Chapters  have  been  added  on  compressed-air  and  refrigerat- 
ing machines,  to  provide  for  the  study  of  these  important  sub- 
jects in  connection  with  the  theory  of  thermodynamics. 

Wherever  direct  quotations  have  been  made,  references  have 
been  given  in  foot-notes,  to  aid  in  more  extended  investiga- 
tions. It  does  not  appear  necessary  to  add  other  acknowledg- 
ment of  assistance  from  well-known  authors,  further  than  to 
say  that  their  writings  have  been  diligently  searched  in  the 
preparation  of  this  book,  since  any  text-book  must  be  largely 
an  adaptation  of  their  work  to  the  needs  of  instruction. 

C.  H.  P. 

MASSACHUSETTS  INSTITUTE  OF  TECHNOLOGY, 
May,  1889. 


TABLE   OF  CONTENTS. 


CHAPTER   I. 

PAGE 

THERMAL  CAPACITIES,  .......        i 

CHAPTER   II. 
FIRST  LAW  OF  THERMODYNAMICS,    .  .  .  .  .      n 

CHAPTER   III. 

SECOND  LAW  OF  THERMODYNAMICS,  .  .  .  .  .19 

CHAPTER   IV. 

NON-REVERSIBLE  PROCESSES,  .  .  .  .  .  -34 

CHAPTER   V. 

FUNDAMENTAL  EQUATIONS,    .......      37 

CHAPTER  VI. 

PERFECT  GASES,      ,   .  .  .  .  ..  .  ,  .45 

CHAPTER    VII. 
SATURATED  VAPOR,    ........      68 

CHAPTER  VIII. 

SUPERHEATED  STEAM,  -          .  .  .  .  .  .  .115 

CHAPTER   IX. 
FLOW  OF  FLUIDS,.       .  ,  .  ...  .  .  .129 

CHAPTER  X. 
INJECTORS,       .........    144 

v 


yi  TABLE   OF  CONTENTS. 

CHAPTER   XI. 

PAGE 

HOT-AIR  ENGINES,      ...  »   -.       «  .  „          y          .170 

CHAPTER  XII. 
THE  STEAM-ENGINE,          /  .  .  .  .  .  .178 

CHAPTER  XIII. 
COMPOUND  ENGINES,  .  .  .  .        .  «...    204 

CHAPTER  XIV. 

TESTING  STEAM-ENGINES,     /.  ...          .  .  .  .    225 

CHAPTER  XV. 
TESTS  OF  SIMPLE  STEAM-ENGINES,   .  .  .  .  .  .    244 

CHAPTER  XVI. 
TESTS  OF  SIMPLE  AND  COMPOUND  ENGINES,          .  .  .  .     269 

CHAPTER   XVII. 

HIRN'S  ANALYSIS,       .  .  .  .  .  ,  .  .    301 

CHAPTER   XVIII. 

VARIOUS  STEAM-ENGINE  TESTS,      \ «  \  .   .    .  .  .  .  .     338 

CHAPTER  XIX. 
FRICTION  OF  ENGINES,  ....          y          •  395 

CHAPTER  XX. 
COMPRESSED  AIR,       . .  .  .  »  .  .  .405 

CHAPTER  XXI.        ; 
REFRIGERATING  MACHINES,   .  .  .  •  434 


INDEX. 


PAGE 

Absolute  scale  of  temperature,  .  .  .  .  .  .25 

Absolute  scale  of  temperature  and  air  thermometer,         .  .  .  58 

Absorption  refrigerating  apparatus,     ......  460 

Acceleration  of  gravity,      .  .  .  .  _,  .  .  47 

Adiabatic  expansion  of  vapor,  external  work,  .  r  .  .   in 

Adiabatic  line  for  superheated  steam,        ."        .  .  .  .          126 

Adiabatic  lines,  .....  ..*  ,  .  14 

Adiabatic  lines  for  gases,    .  .  .        •    ,  ^  .  .  53 

Adiabatic  lines  for  vapor,  construction  of,      .  .  '    '  .  .  109 

Adiabatic  of  liquid  and  vapor,        .  5          .  .  .  .  .107 

Alsatian  experiments  on  friction  of  engines,  ...  .  .  396 

Alternative  method,  .  .  .  .  .  .  29 

Ammonia,  properties  of,  ........  456 

Application  of  first  law,      ...  .  .  .  .  .  37 

Application  of  first  and  second  laws  to  gases,  .  .  .  .48 

Application  of  first  law  to  superheated  steam,      .  .  .  .116 

Application  of  second  law,        .  .  .  .  .  '39 

Application  of  second  law  to  superheated  steam,  .  .  .          117 

Air-compressor,  calculation,     .  .  .  .  .  .  418 

Air-compressor,  compound,  .  .  .  .  .  .411 

Air-compressor  cylinder,  volume  of,    .  .  .  .  .  .  410 

Air-compressor,  displacement,       ...  .  .  .         414 

Air-compressor,  distribution  of  work,  .....  416 

Air-compressor,  effect  of  clearance,  .....          407 

Air-compressor,  fluid  piston,    .  .      •     .  .  .  .  .  413 

Air-compressor,  power  exp'ended,  .....         405 

Air-compressor,  tests  on,          .  .  .  .  .  .  •  415 

Air-engines,  .  .  .  .  .  .  .  .-170 

Air,  Fleigner's  equations  of  flow,         ......    135 

Air-pumps,  .  .  .  .  .  .  .  .  .417 

Air-refrigerating  machine,        .......  434 

Air  thermometer,  comparison  with  absolute  scale,  ...  58 

Air  thermometer,  reduction  to  absolute  scale,  ;  .  .  .60 

vii 


viii  INDEX. 

PAGE 

Bache,  tests  on,          •    ^  .  .  .  .  .  .  .  268 

Barrel  calorimeter,  .......         229 

Barrus  continuous  calorimeter,  ;  ,  .  .  .  .231 

Barrus  superheated  steam  calorimeter,      .  ;»  .  .  .          234 

Bell-Coleman  refrigerating  machine,  .  .  .  .  .  .  464 

Boiler  efficiency,      ...  .  .  .  .  .          241 

British  thermal  unit.     .  .  .  .  .  .  .  .11 

Calculations  for  compound  engine,  .  .  .  .  .          212 

Calculations  for  triple-expansion  engine,         .  .  .  .  220 

Calculation  of  air-compressor,        ......         418 

Calculation  of  air-refrigerating  machine,         ......  438 

Calculation  of  compressed-air  engine,        .....         430 

Calculation  of  compression-refrigerating  machine,     .  .  .  .  446 

Calorimeter,  .  '.  '.  .  .  .  .  .         229 

Calorie,  .  '.  *.  .  .  '         .  .  .  .  .11 

Calorimeter,  barrel,         '".'.  .  '»  .  .  .  .         229 

Calorimeter,  continuous,  .  "...  .  .  .  .  231 

Calorimeter,  superheated  steam,    .  .  ,  .  .  .         235 

Calorimeter,  throttling,  *.  .  .  ,  ,  .  .  237 

Capacities,  thermal,  .  .  .  .  '.  ,  .  6 

Carnot's  cycle  for  gases,  .  .  >%          .  ".  .  .  -55 

Carnot's  engine,        .  .  \  \  .  .  .  .19 

Carnot's  function,  .  .  .  .  .  .  .24 

Carnot's  principle,  .  .  .  .  .  .  .  .  23 

Carnot's  principle,  generalization,        .  .  "..-».  •  -32 

Coefficient  of  dilatation,      .  .    •         .  .»  .  .  .  45 

Characteristic  equation,  .  .  .  .  ,  .  «      2 

Characteristic  equation  for  superheated  steam,      .  .  •  *          118 

Characteristic  equation,  represented  by  a  surface,       .  .  .  .      5 

Closed  cycle,  ........  22 

Compressed  air,  ........  405 

Compressed  air,  contraction  after  compression,    ....          409 

Compressed  air,  effect  of  clearance,     ......  407 

Compressed  air,  interchange  of  heat,         .....         410 

Compressed  air,  temperature  after  compression,        ....  409 

Compressed-air  transmission,  efficiency,  .....          432 

Compressed-air  engine,  .....  ,  425 

Compressed-air  engine,  calculation,  .  .•  .  430 

Compressed-air  engine,  compound,      ......  429 

Compressed-air  engine,  consumption,        ....  427 

Compressed-air  engine,  final  temperature,       .....  427 

Compressed-air  engine,  interchange  of  heat,         ....          428 

Compressed-air  engine,  moisture  in  cylinder,  .  .  .  428 

Compressed-air  engine,  power  of,  ...  .         425 

Compressed-air  engine,  volume  of  cylinder,    .....  428 

Compression-refrigerating  machine,  .....          444 


INDEX.  ix 

PAGE 

Compound  air-compressors,      .             .     •                     .             .             .  .411 

Compound  air-engine,         .......  429 

Compound  engine,         .             .             »            ,            .             .             .  .  204 

Compound  engine,  calculations  of,             .....  212 

Compound  engine,  Hirn's  analysis,     .          •  •             »            .             .  .  222 

Compound  engine,  ratio  of  cylinder,          .            »            .             ,             .  210 

Compound  engine,  tests  on,     .             .            »             .             .             .  .  309 

Compound  engine  with  receiver,    .             .             ,             .             .             .  207 

Compound  engine  without  receiver,     .             ».-          .             .             .  .  206 

Condenser,  ejector,              .             .            .             .             .             ,             .  167 

Condensers,  cooling  surface,    .             .             .             .             .             .  .   199 

Condensers,  jet,       .'•           .            <            •             .             .             ,             .  199 

Condensers,  surface,      .             ....             .             .             ,  .   196 

Constants  for  superheated  steam,  .             .             .             .             ,             .  120 

Continuous  calorimeter,           '•••'.             .            .             .             ,  .  231 

Cost  of  power,          .            .             .             .             .             .             ,             .  241 

Critical  temperature,     .             ...             .             .             ,  .  101 

Cycle,  closed,           ...             .             .             .             .             .  22 

Cycle,  reversible,          ...             .             .             .             .             ,  .21 

Dallas,  tests  on,       .            ..            .             .             .             .             ,  269 

Density,               .             .             ...             .             ,             ,  .2 

Density  of  mercury,             .......  76 

Density  of  vapors,          .             .                          .             .             ,             .  .96 

Demon's  tests  of  absorption  refrigerating  machine,          .             ,             .  469 
Designing  steam-engines,          .......  200 

Dexter,  tests  on,                   .             .             .             .             .             .             .  269 

Differential  coefficient  -7 ,                                  .             .  80,  82 
at 

Dilatation,  coefficient  of,     .  .  .  .  .  .  .45 

Distribution  of  engine  friction,             ;             .             .             .             .  .  400 

Dixwell's  tests,         .             .             .            ',    •         .             .             .             .  256 

Donkin  engine  tests,      .                       -\            .             .             .             .  .  338 

Donkin  mill-engine,             .......  344 

Donkin  pumping-engine,           .             '.             .             .             .             .  .  346 

Duty  test  of  Leavitt  engine,            ......  293 

Dynamometers,              .                          .             .             .             .             .  .  227 

Effects  of  the  transfer  of  heat,        .            .            .            .            .  ir 

Efficiency,           ........  .22 

Efficiency  of  boiler,              .......  241 

Efficiency  of  compressed-air  transmission,      .....  432 

Efficiency  of  ideal  steam-engine,    ......  180 

Efficiency  of  reversible  engines,            .             .             .             .             .  .28 

Efficiency  of  steam-engine,  .....  239,  366 

Ejector,  ..........   167 

Ejector  condenser,  ........  167 

Emery,  tests  of  engines,  .....  268,  271,  272 


X  INDEX. 

PAGE 

Energy,  graphical  representation  of  change,   .  „  ,  .  .16 

Energy,  intrinsic,  superheated  steam,        .  123 

English's  steam-engine  tests,    .  .  .  .  .  .  351 

English's  tests  on  initial  condensation,      .  .  «  .         359 

Entropy,  ......          • ,          ,   .  .17 

Entropy  of  a  liquid,          > ••  » -. .          .  .  .  .  ,.  ...        106 

Entropy  of  a  liquid  and  vapor,  .  .  .  .  .  .    105 

Entropy  of  gases,     ...  .  .  .  .  .  55 

Entropy  of  superheated  steam,  ....          .,.,,.  .    119 

Entropy,  scale  of,    .  .  .  .  .  .  .26 

Engine,  Carnot's,  .  .  .  .  .  .  .  19 

Engine,  compressed-air,      .  .  .  .  .  .         ,   *         425 

Engine,  efficiency  of,     .  .  .  .  .  .  .  .22 

Engine,  efficiency  of  reversible,      ......  28 

Engine,  Ericsson's,        .    '       •  .  .  .  .  .  .  .   175 

Engine,  friction  of,  .  .  .  .  .  .  395 

Engine,  gas,       .  .  .  .  .  .  .  .  .   176 

Engine,  hot-air,        .  ,  ,  .  .  •  .  .  .          170 

Engine,  reversible,         .  '          .,  .  .  .  .  .  .21 

Engine,  steam,  .  ,  .  .  .  .  .178 

Engine,  Stirling's,  ...  .  .  .  .  .   172 

Ericsson's  hot-air  engine,   .  .  •  .  .  .  .  .175 

Eutaw,  tests  on,  ..  ^  .....  253 

Exhaust-steam  injector,      .......          162 

Experiments  on  flow  of  steam  at  Massachusetts  Institute  of  Technology,    .   140 
Exponent  for  superheated  steam,  .....  117,119 

Exponential  equation,    .  .  .  .  .  .  .  .102 

External  latent  heat  of  vapors,       ......  91 

External  work  during  adiabatic  expansion  of  vapor,  .  .  .   in 

Fan-blowers,  ........         414 

First  and  second  laws  combined,          .  .  .  .  .  .     41 

First  law,  application  of,  .  .  .  .  37 

First  law,  application  to  superheated  steam,  .  .  .  .116 

First  law,  application  to  vapors,      ......  93 

First  law  of  thermodynamics,  .  .  .  .  .  .11 

Fleigner's  equations  for  flow  of  air,  .....          135 

Flow  of  air,  Fleigner's  equations,         ......   135 

Flow  of  air,  maximum  velocity,      ......          136 

Flow  of  air  through  porous  plug,          .  .  .  .  .  -59 

Flow  of  air,  Weisbach's  experiments,         .....          137 

Flow  of  fluids,    .........  129 

Flow  of  gases,          ........          131 

Flow  of  incompressible  fluids,  ......   129 

Flow  of  saturated  vapor,     .......          138 

Flow  of  superheated  steam,       .......   141 

Fluid  piston  air-compressor,  ......         413 


INDEX.  xi 

PAGE 

Fluids,  flow  of,         .....  o  •  .          129 

Fluids  for  refrigerating  machines,         ......  450 

Friction  of  engines,    ........       395 

Friction  of  engines,  Alsatian  experiments,          v  .  .  .  396 

Friction  of  engines,  Thurston's  experiments,  ,  .  .  .  400 

Function,  Carnot's,  .......  24 

Fundamental  equations,  ,  .  .  .  .  .  -     37 

Gas-engines,  .  •  *  *  .  .  .  .          176 

Gases,     .  .  *  •    ,         •  •    ,         .  .  .  -45 

Gases,  adiabatic  lines,          .  *. •  ,         .  .  *  .  •  53 

Gases,  Carnot's  cycle,  .  .  *  .  .  .  .  -55 

Gases,  entropy,        .  .  .  «  .  .  .  .  55 

Gases,  flow  of,    .  .  .  .  •  .  .  .  .  131 

Gases,  general  equations,    .  V  •  .  •  .  .50 

Gases,  intrinsic  energy,       .  ,,.          '.,  •  ....  55 

Gases,  isodynamic  lines,  .  -       •-*  •  •  •  •  •     52 

Gases,  isoenergic  lines,  .'•[*  .  .  .  .  .  52 

Gases,  isothermal  lines,  .          ,  „».  .  •  .  .  51 

Gases,  ratio  of  specific  heats,  ......         63 

Gases,  specific  heat,  .«•....  48 

Gases,  specific  volume,  .  •  .  .  .  .  .46 

Gases,  thermal  capacities,  .......  49 

Gallatin,  tests  on,  .  ,  .  .  .  .  .  273 

Gauges,         .........          227 

General  equations,         ........       6 

General  equations  for  gases,  .  ,  ....  50 

General  equations,  superheated  steam,  .  .  .  .  .118 

Giffard  injector,        .  .  .  .  .  .  .  .          154 

Gleam,  tests  on,  ........  283 

Graphical  representation  of  change  of  energy,      .  .  .  .  16 

Gravity,  acceleration  of,  ...  .  .  .  -47 

Hallauer's  method  of  calculation,  .  .  .  .  .          304 

Hallauer's  tests  of  compound  engines,  .....  309 

Hallauer's  tests  of  marine  engines,  -,  ....          309 

Hallauer's  tests  of  simple  engines,      .  .  ,  .  .  .  301 

Hancock  injector,    ........          156 

Harris-Corliss  engine,  tests  on,  ......   263 

Heat,  effects  of  transfer,     .  .  .  ,  .  .  .11 

Heat,  latent,  of  expansion,        .  .  .  .  .  .  .6 

Heat,  mechanical  equivalent,          .  .  .  .  .  .n 

Heat  of  the  liquid,          .  .  .  .  .  .  .  82,  84 

Heat,  specific,          ........  6 

Hill,  tests  on  engines,  ........  263 

Hirn's  analysis,  calculation  of  problem,     .  .  .  .  .191 

Hirn's  analysis  for  compound  engine,  .....  222 

Hirn's  analysis  for  steam-engine,  ......          185 


xii  INDEX. 

PAGE 

Hirn's  analysis,  tests  of  engines,          .            .            .            .             .  .301 

Hirn's  experiments  on  superheated  steam,                       .            .            .  124 

Hot-air  engine,  Ericsson's,    .            -»             .             .            *  ,          .  .175 

Hot-air  engine,  Stirling's,          »             .             .            .        ;    *'.;;        *r  .   172 

Hot-air  engines,     *.           «.         -    ,f            .             .             .             •             .  170 

Hot-air  engines  of  maximum  efficiency,              .            .         . •-';            .  170 

Indicated  steam  consumption,           ^            .            .            .  .  369 

Indicators,    .             .    •        .    •        . •   -        .    •         .            .    •       ..             .  228 

Injector,              .    •        .    •        .             • .   «        •            •    '        *    •        .    •  .   144 

Injector  as  a  pump,              .             .            •    •        .           .»<?-'        .             .  163 

.Injector,  automatic,       .    <         .            •    '        *    '        .     •        .             v  .   154 

Injector,  double,      .             .             .            .             .                         «    '        *  •      156 

Injector,  exhaust  steam,            .             .                          .    *        .    •        .-•  .   162 

Injector,  fixed  nozzle,          .             .             .          ..•     -        .            *            .  154 

Injector,  Giffard's,       -»  .  .  .  .  ...   154 

Injector,  Hancock,             *.             .             .           >.          •«            •             *  -:     156 

Injector,  Korting,         *.             .           ',    .        .           »•   .         *            *  .   157 

Injector,  Mack,     •  ••.           ».             .             .             .             .            v            «  153 

Injector,  limits  of  action,          .             ,             .            .             •            .  -152 

Injector,  Sellers,      .             .             .             .            ,  l          .             *  -          .  154 

Injector,  sizes  of  orifices,          .             *  -/<        .            •            •            .  .  150 

Injector,  tests  of,     .         •    .     •        .             .           ,»     •        .            .             .  158 

Injector,  theory  of,        .         ;    ,             .        '    .    <        .     •     '    .  .          .  .  146 

Injector,  velocity  of  steam  jet,       .             .             .            .                          .  146 

Injector,  velocity  of  water  jet,              «            .             •            .             .  .  148 

Injector,  water,        .             .             .             .           •.»    •.         .             .             .  165 

Injector,  water  fed  per  pound  of  steam,          .....   147 

Initial  condensation,            .......  359 

Interchange  of  heat,  compressed-air  engine,  .....  428 

Interchange  of  heat  in  air-compressors,    .....  410 

Internal  latent  heat  vapors,       ......  91,  100 

Intrinsic  energy  of  gases,    .......  55 

Intrinsic  energy  of  superheated  steam,             .             .  .123 

Isodynamic  lines,     ........  13 

Isodynamic  line  for  gases,        .             .             .             .             .            .  .52 

Isodynamic  line  for  steam,              ......  104 

Isodynamic  line  for  superheated  steam,           .            .             .             .  .127 

Isodynamic  line  for  vapors,             ......  104 

Isoenergic  line  for  gases,           .             .             .             •            .             .  .     52 

Isoenergic  line  for  steam,                ......  104 

Isoenergic  line  for  superheated  steam,            .            .            .            .  .127 

Isoenergic  line  for  vapors,               ......  104 

Isometric  lines,               .......  .     13 

Isopiestic  lines,        .             .             .             .            .            .             .        :    *  -        13 

Isherwood,          ........       244,  283 

Isothermal  lines,      .  .  .  .  .  .  .  .13 


INDEX.  xiii 

PAGE 

Isothermal  line  for  gases,           .            .            .            e            •            .  .51 

Isothermal  for  steam,           ......             .  103 

Isothermal  line  for  superheated  steam,             '••",         •             •             •  •   I27 

Isothermal  for  vapors,          .             .            „ •:;  l    -  ~i;            .             .             .  103 

Jet  condensers,  .             .             .            •            •            -^--          •             •  •   199 

Joule  and  Thomson's  experiments,              *           '.             .             .  59 

Joule's  equivalent,           .             .             .             .             *             .             .  .88 

Kilogram,  weight  of,             ,\           .             .             •             *             .             .  76 

Korting  injector,             *     '         .             .             .             •             .             .  .   157 

Kraft's  tests  of  air-compressors,      »   ,         «            .             .             .             .  415 

Latent  heat  of  expansion,           .             »J          •    •         •             •             •  .6 

Leavitt  pumping-engine,      .            ,             •    :•        ....  293 

Leila,  tests  on,    ...             .             .             .             .             .  .   283 

Length  of  meter,      .             .             «            .....  76 

Line  of  constant  steam  weight,               .            .             .             .             .  .   102 

Lines,  adiabatic,       .-,''.             .             .             .             .             .  14 

Lines,  isoenergic,                          ,             «             .             .             .             .  13 

Lines,  isopiestic,       .             •             >             .             .             .             .             .  13 

Lines,  isometric,              .             ....             .             .             .  13 

Lines,  isothermal,    .           -.    .       <*•           •             •             •             •             •  J3 

Lines,  thermal,  .«•.«..             .             .  13 

Liquid  and  vapor,  adiabatic  line,     ......  107 

Liquid,  entropy  of,         «             .             ,             .             .             .             .  .   106 

Liquids,  specific  volumes  of,  •  .  .  .  .  .90 

Mack  injector,    .             .             .                          .             .             .             .  .1*53 

Mackinaw,     .             '.             .             .             .             .             .             .             .  249 

Mair's  steam-engine  tests,           .             »            .             .             .             .  .318 

Marine  engines,  tests  on,      .                          .             .             .             .             .  309 

Massachusetts  Institute  of  Technology  steam-engine  tests,      .             .  .  333 

Massachusetts  Institute  of  Technology  experiments  on  flow  of  steam,  .       140 

Massachusetts  Institute  of  Technology  tests  of  injectors,               .             .  159 

Massachusetts  Institute  of  Technology  tests  on  steam-engines,         .  385 

Maximum  velocity  of  flow  of  air,    .            ..             .             .             .             .  136 

Mechanical  equivalent,  Joule's,              ...             •             .             .  .88 
Mechanical  equivalent,  Rowland's,  .             .             .             .             .             .85 

Mechanical  equivalent  of  heat,  .          ,,»    '•                     .             .             .  II,  87 

Mercury,  density  of,              .            ,,             .             .             .             .             .  76 

Meter,  length  of,              .             .             .             .             .             .             .  .76 

Michigan,  tests  on,  .             .             .             .             .             .             .             .  244 

Millers'  exhibition,          .             ,             .             ,             .             .             .  .  263 

Napier's  formulae  for  flow  of  steam,      .             .             .             .             .  .140 

Non-reversible  processes,    .......  34 

Pambour's  method,  friction  of  engines,  .....  395 

Perfect  gases,            ........  45 

Pictet's  fluid,       .........  459 

Porous  plug,  flow  through,               ......  59 


xiv  INDEX. 

PAGE 

Power,  cost  of,  .             .             •            •            »             .            .             .  .  241 

Power  expended  in  compressing  air,           .             .             .           v           .  405 

Power  of  compressed-air  engine,           .             .             .            .             .  .  425 

Pressure,  effect  of,  on  change  of  state,        ,            .             ,  -          .             .  101 

Pressure  of  saturated  steam,      .           v.             .             .            .             .  75,  76 

Pressure  of  steam  at  Paris,               .             .  .          .            .             .             .  73 

Pressure  of  vapors,         .             .             *            .             .            •             .  68,  79 

Pressure,  specific,     .             .                        '  *             .             .             .             .  2,  47 

Principle,  Carnot's,         .             .             .            •            .             .            .  .23 

Processes,  non-reversible,                 .            .             .             .            .             .  34 

Rankine's  equation  for  pressure  of  steam,         .            .   '         .             .  -78 

Ratio  of  cylinders,  compound  engines,        .             .            *            .            .  210 

Ratio  of  specific  heats,                ."            .             .             .            ,'            ,  -63 

Regnault's  equations  for  steam,       .             .             .            .            .            .  71 

Refrigerating  machines,             .             .            .                         ,            .  .  434 

Refrigerating  machines,  absorption,            .             .            ...  460 

Refrigerating  machines,  air,       .             » .':         .             .          •  .             «  -  .  434 
Refrigerating  machines,  calculation,            .             .             .            .              438,446 

Refrigerating  machines,  compression,                .             .             .            .  .  444 

Refrigerating  machines,  extraction  of  moisture,     .             .            .            .  437 

Refrigerating  machines,  fluids,               .             .             .            .            i  .  450 

Refrigerating  machines,  vacuum,    .             .             .             .             .            .  462 

Refrigerator,        .«            .             .             .             .             .             .             .  19 

Relations  of  thermal  capacities,       .             .            .            .             .        ; :-  *  7 

Reversible  cycle,             .             .             .            .            .            .            .  .21 

Reversible  engine,    .         '     .             ,     :        .             .             .             .           -.  21 

Reversible  engines,  efficiency  of,                        .             .            .             .  .28 

Reynolds-Corliss  engine,      .......  263 

Rotary  blowers,  ........  414 

Rowland's  experiments,        .  .  .  .  .  .  .85 

Rowland's  equivalent,     .             .             .             .            .             .             .  .88 

Rowland,  reduction  of  air  thermometer,     .....  60 

Rush,  tests  on,    .........  269 

Saturated  vapor,  flow  of,      .             .             .            .             .             .             .  138 

Saturated  vapors,  .  .  .  .  ....     68 

Scale  of  entropy,      .             ...             .             .             .             .  26 

Scales,     ..........  228 

Schroter's  tests  of  refrigerating  machines,  .                         ,            .             .  463 
Seaton's  multipliers  for  steam-engine  design,  ....        201,  221 

Second  law,  application  of,               ......  39 

Second  law,  application  to  superheated  steam,              .            .             .  .   117 

Second  law,  application  to  vapors,  ......  94 

Sellers  injector,  .             .             .            .            .            «            •             •  •  T54 

Siesta,  tests  on,         .             .            .             •            •             •                          •  283 

Sound,  velocity  of,         .             .             .             •            •             •             •  .60 

Source  of  heat,          ........  19 


INDEX. 


Specific  heat,       .........       6 

Specific  heat  of  gases,  .......  48 

Specific  heat  of  superheated  steam  at  constant  volume,  .  .  .122 

Specific  heat  of  steam,         ..,.>.  .  .  .  .  95 

Specific  heat  of  water,  „   ' '    '    .  -.-         .  .         •    .  .  82,86 

Specific  heat  of  vapors,        .  .  .  .  .  .  .  95 

Specific  heats  of  gases,  ratio,     .  »(  .  .  .  .  .     63 

Specific  heats  of  water  and  steam,  .  «  .  ...  93 

Specific  pressure,  .  t  .  .  .  .  .  2,  47 

Specific  volume,        ........  2 

Specific  volume  of  gases,  .  .  .  .  .  .  .46 

Specific  volume  of  vapors,   .  »  .  .  .  .96 

Specific  volumes  of  hot  liquids,  .  .  ,  .  .  .90 

Standard  temperature,          .  ,*  ,x  .  .  .  .  87 

Steam,  application  of  first  law,  *  .  .  .  .  -93 

Steam,  application  of  second  law,  ......  94 

Steam  consumption,  measurement  of,  .  .  .  .  .  .  229 

Steam,  curve  of  constant  weight,    .  .  .  .  .  102 

Steam,  entropy  of,          ,  ...  ......   105 

Steam,  flow  of,          •  .  *  .  .  .  .  .          1*38 

Steam,  internal  and  external  heat,         .  .  .  .  .  .     91 

Steam  isodynamic  line,         .  .  .  .  .  .  .          104 

Steam  isoenergic  line,    .  ...  .  .  .  .   104 

Steam,  isothermal,   .  .  .  .  .  .  .  .103 

Steam,  Napier's  equations  for  flow,       ......   140 

Steam,  pressure  of,  .  .  .  .  .  .  .  75,  76 

Steam,  pressure  at  Paris,  .  «  .  .  .  .  '73 

Steam,  Rankine's  equation,  .  ..;•..  •  •  •  78 

Steam,  Regnault's  equations,     .  .  .  .  .  .  71 

Steam,  specific  heat  of,         .  .  » . ' .;  .  .  .  95 

Steam,  superheated,        .  .  ,  .  .  .  .  .115 

Steam,  total  heat,     .  .  *  .  .  .  .88 

Steam-engine,     .  .  .  .  .  .  .  .  .178 

Steam-engine,  actual,  .  .  .  .  .  .  .          181 

Steam-engine,  Carnot's  cycle,    .  ...  .  .  .  .178 

Steam-engine,  compound,    .......          204 

Steam-engine,  consumption  for  perfect  cycle,  .  .  .  .  .180 

Steam  engine  designing,       .  .  .  .  .  .  200 

Steam-engine  efficiency,  .......   239 

Steam-engine  indicators,      .......          228 

Steam-engine,  Hirn's  analysis,  .  .  .  .  .  .  .185 

Steam-engine,  testing  of,  .  .  .  .  .  .          225 

Steam-engine,  Seaton's  multipliers,       ......  201 

Steam-engine,  triple  and  quadruple  expansion,        ....          209 

Steam-engine,  water  in  the  cylinder,     ......  333 

Stirling's  hot-air  engine,       .  .  .  .  .  .  .172 


xvi  INDEX. 


PAGE 


Superheated  steam,         .  .  .  .  .  .  .  .  115 

Superheated  steam  adiabatic  line,    .  .  .  ,  .  .          126 

Superheated  steam,  application  of  first  law,      .  .  " -.  .  .116 

Superheated  steam,  application  of  second  law,        .        ^     ,  .  .          117 

Superheated  steam,  characteristic  equation,      .  .  -"-.         -^  V''         .   118 

Superheated  steam,  comparison  with  experiments,         :    »•          .   '         .          124 
Superheated  steam,  entropy,      .  .  .  .  .  .  .119 

Superheated  steam,  flow  of,  ....         >•'".  .          141 

Superheated  steam,  general  equations,  .  .  .*  .  .118 

Superheated  steam,  Hirn's  experiments,     .  .  .  .-'  '        .         124 

Superheated  steam,  intrinsic  volume,    .  .  '.,  .          !-.  .   123 

Superheated  steam,  isodynamic  line,  .  .  .  -f    •-    '     .          127 

Superheated  steam,  isoenergic  line,       .  .  .          '    ,;  -          ,  .   127 

Superheated  steam,  isothermal  line,  .  •..        '    .  ,"          .          127 

Superheated  steam,  specific  heat  at  constant  volume,  .  .        ll   >.  .  122 

Superheated  steam,  thermal  capacities,       .  .  .  %'        ;    .    -     n8 

Superheated  steam,  total  heat,  .  .  .  .  .  .  .123 

Superheated  steam,  values  of  constants,      .  .  .    .         .-        V1       120 

Sulphur  dioxide,  properties  of,  .  .  .  ,  ',  .  452 

Surface  condensers,  .  .  .  .  .  ,          v  .•'•       196 

Tate  and  Fairbairn's  experiments,         .  .  .  .  .  .98 

Temperature,  ........  2 

Temperature,  absolute  scale  of,  .  .  .  .  .  .25 

Temperature,  definition  of,  .  .  .  «  .  .25,  32 

Temperature,  standard,  .  .  .  .  .  .  .87 

Temperature,  Thomson's  scale,       ...  ...  25 

Testing  steam-engines,  ........  225 

Tests  of  absorption-refrigerating  machine,  ....         469 

Tests  of  air-compressors,  .  .  .  .  .  .  .415 

Tests  of  Bell-Cole  man  refrigerating  machine,         ....         464 

Tests  of  compression-refrigerating  machines,  .....  464 

Tests  of  injectors,    .  .  .  .  .  .  .  .158 

Tests  of  refrigerating  machines,  Schroter,        .....  463 

Tests  of  Sellers'  injector,      .  .  .  .  .  .  .159 

Tests  on  automatic  engines,       .......  263 

Tests  on  Donkin  engines,    .......          338 

Tests  on  Donkin  mill-engine,    .......  344 

Tests  on  Donkin  pumping- engine,  .......         346 

Tests  on  compound  engines,      .......  309 

Tests  on  Leavitt  engine,       .......          293 

Tests  on  marine  engines,  .......   309 

Tests  on  initial  condensation,  ...'...          359 

Tests  on  simple  steam-engines,  ......  244 

Tests  on  simple  and  compound  engines,     .....          268 

Tests  on  steam-engines,  Dixwell's,        ......   256 

Tests  on  steam-engines,  Mair's,       .  .  .  .  .  .          318 


INDEX.  xvii 


Tests  on  steam-engines,  English's,         .  .  „  .  •  351 

Tests  on  steam-engines,  Institute  of  Technology,  .  .  ,  333>  385 

Tests  on  steam-engines,  various,  ......  338 

Tests  on  the  Bache,  .  •  268 

Tests  on  the  Eutaw,        .  .  ....  253 

Tests  on  the  Gallatin,  .  .  272 

Tests  on  the  Leila,  Siesta,  and  Gleam,  .....  283 

Tests  on  the  Mackinaw,        .......          249 

Tests  on  the  Michigan,  ........  244 

Tests  on  the  Rush,  Dexter,  and  Dallas,       .....         269 

Tests  on  Willans'  engine,  .......  364 

Tests  on  Worthington  pumping-engine,      .  .  .  .  .         387 

Theory  of  injectors,        ........  146 

Thermal  capacities,  .  .  .  .  .  .  .  .  5 

Thermal  capacities  of  gases,      .  .  .  .  .  .  -49 

Thermal  capacities,  relations  of,      .  .  .  .  .  ;  6 

Thermal  capacities,  superheated  steam,  .  .  .  .  .118 

Thermal  lines,  ........  13 

Thermal  unit,      .  .  .  .  .  .  .  .  .     II 

Thermodynamics,  first  law,  .  .  .  .  .  .  n 

Thermodynamics,  second  law,  .  .  .  .  .  .  19,  23 

Thermometers,         .  .  .  .  .  .  .  .          227 

Thomson's  scale  of  temperature,  .  .  .  .  .  .25 

Thomson  and  Joule's  experiments,  .....  59 

Throttling  calorimeter,  ........  237 

Thurston's  experiments  on  friction  of  engines,        ....         400 

Total  heat  of  steam,       .  .  .  .  .  .  .  .88 

Total  heat  of  superheated  steam,     .  .  .  .  .  .123 

Total  heat  of  vapors,      .  .  .  .  .  .  .  .88 

Triple-expansion  engine,  calculations,         .....          220 

Triple-expansion  engines,          .......   209 

Unwin,  test  of  pumping-engine,       ......          387 

Vacuum  refrigerating  apparatus,  ......  462 

Value  of  R,  .  .  .  .  .  .  .  .  .47 

Vapor  and  liquid,  adiabatic  line,  ......   107 

Vapor,  entropy  of,    .  .  .  .  .  .  .  .          105 

Vapor,  flow  of,   .  .  .  .  .  .  .  .  .  138 

Vapors,          .........  68 

Vapors,  application  of,  .  .  .  .  .  .  .  •     94 

Vapors,  application  of  first  law,       ......  93 

Vapors,  density  of,  .  .  .  .  .  .  .96 

Vapors,  internal  and  external  heat,  .  .  .  .  .91 

Vapors,  isodynamic  line,  .......   104 

Vapors,  isoenergic  line,        .......          104 

Vapors,  isothermal  line,  .......   103 

Vapors,  pressure  of,  .  .  .  .  .  .     68,  79 


xviii  INDEX. 

PAGE 

Vapors,  specific  heat,     .             ,            •            •            .            .            .  -95 

Vapors,  specific  volume  of,              ......  96 

Vapors,  total  heat,          .             .            .             .            ,            *             .  .89 

Velocity  of  sound,    .             .             .             .             •         •«.'•            .  60 

Volume  of  air-compressor  cylinder,      .             .             .            ,  •          .  .410 

Volume  of  compressed-air  engine  cylinder,            .             .            .            .  428 

Volume,  specific,  ........       2 

Water  in  the  cylinder  of  steam-engines,      .             .             .            »•           .  333 

Water,  specific  heat  of,               .             .             .             .             .            .  .82 

Water  injector,          .             .             .             .            .            .            .            .  165 

Weight  of  kilogram,       .             .             .             .            .            .        •    ,-  .76 

Weirs,           .             .             .             .            .            .            .                         .  228 

Weisbach's  experiments  on  flow  of  air,              .            ,            »            .  .   137 

Wheelock  engine,  tests  on,               .             .            .            .            .            ,  263 

Willans' steam-engine  tests,       .             .            .            .            .,'»>•  .  364 

Zeuner's  equations,  .             .             ......  42 

Zeuner's  equations  for  internal  heat,    ......  100 


THERMODYNAMICS  OF  THE  STEAM-ENGINE. 


CHAPTER  I. 

THERMAL   CAPACITIES. 

THE  object  of  thermodynamics,  or  the  mechanical  theory 
of  heat,  is  the  solution  of  problems  involving  the  action  of 
heat,  and,  for  the  engineer,  more  especially  those  problems  pre- 
sented by  the  steam-engine  and  other  thermal  motors.  In  this 
work  the  discussion  of  the  actual  nature  of  heat  and  the 
rationale  of  its  various  actions  will  be  purposely  avoided,  and 
attention  will  be  given  rather  to  the  calculation  of  the  results 
of  such  actions. 

Some  conceptions  already  familiar  will  appear  in  a  some- 
what different  light ;  and  some  new  conceptions  will  be  pre- 
sented. It  will  be  found  that  some  of  the  latter  are  susceptible 
of  more  concise  definition  than  others  that  are  now  more 
familiar.  Also  some  methods  of  operation  will  be  employed 
which  may  seem  more  abstract  than  those  commonly  used  in 
engineering.  The  student  will,  however,  recognize  them  as 
methods  that  he  has  already  learned,  and  he  will  gain  confi- 
dence in  them  by  familiarizing  himself  with  their  use. 

Effects  of  Heat. — In  general,  the  action  of  heat  on  a 
body  causes  a  change  in  all  the  characteristics  of  the  body,  such 
as  the  density,  tension,  temperature,  elasticity,  refractive 
index,  conductivity,  etc.  When  heat  is  communicated  to  or 
taken  from  a  body,  there  is  a  change  in  the  energy  of  the  body. 
If  a  body  is  supposed  to  be  at  rest,  or  if  its  visible  motion  is 
not  changed  during  the  operation,  and  can  consequently  be 
disregarded,  the  change  of  energy  produced  by  the  communi- 


2  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

cation  or  abstraction  of  heat  may  be  considered  as  a  property 
of  the  body.  The  energy  may  in  general  be  divided  into 
potential  and  kinetic  energy,  in  which  case  each  may  be  a  prop- 
erty of  the  body. 

Characteristic  Equation. — The  assumption  of  the  me- 
chanical theory  of  heat  is  that  if  any  two  of  the  several 
characteristics  or  properties  of  a  body  be  taken  as  independent 
variables,  any  other  can  be  expressed  as  a  function  of  the  two 
independent  variables.  If  x  and  y  are  chosen  as  the  independ- 
ent variables,  and  if  z  is  any  other  characteristic,  then 

z  —  F(x,  y\     or    f(x,  y,  z)  =  o. 

The  form  of  the  function  is  to  be  determined  experimentally  ; 
and  as  yet  the  necessary  experiments  have  been  made  for  only 
a  few  of  the  numerous  functions  that  may  be  indicated  by 
using  the  various  characteristics.  The  most  useful  character- 
istic equation  is 

,f)  =  o, (i) 


in  which/  is  the  pressure,  v  the  volume,  and  /  the  temperature. 

The  pressure  is  assumed  to  be  a  hydrostatic  pressure,  such 
as  a  fluid  exerts  on  the  sides  of  the  containing  vessel  or  on  an 
immersed  body.  We  shall  always  consider  the  pressure  exerted 
by  the  body  rather  than  on  the  body.  .The  pressure  is  stated 
in  units  of  force  per  unit  of  area,  as  pounds  per  square  foot, 
and  is  called  specific  pressure. 

The  density  of  a  body  is  the  weight  of  a  unit  of  volume ; 
for  example,  a  cubic  foot  of  water  weighs  62.4  pounds  nearly, 
or  its  densjty  is  62.4.  The  reciprocal  of  the  density  is  the 
volume  occupied  by  one  unit  of  weight,  and  is  called  the  specific 

volume  ;  the  specific  volume  of  water  being  •? — . 

The  temperature  cannot  be  as  satisfactorily  defined.  The 
common  scales  depend  on  the  properties  of  some  substance, 
such  as  mercury  or  air ;  and  it  can  be  shown  that  the  unit  is 


THERMAL    CAPACITIES.  3 

not  the  same  in  different  parts  of  the  scale.  In  the  course  of 
the  work  it  will  be  shown  th*at  an  absolute  scale  independent 
of  the  substances  used  can  be  constructed  on  thermodynamic 
principles.  It  will  also  appear  that  the  scale  of  the  air  ther- 
mometer coincides  very  nearly  with  the  thermodynamic  scale. 
Again,  the  scale  of  the  mercurial  thermometer  at  medium 
temperature  agrees  with  that  of  the  air  thermometer  sufficiently 
well  for  engineering  work.  To  avoid  difficulty  that  may  arise 
when  we  are  ready  to  establish  the  thermodynamic  scale,  we 
will  abstain  from  accepting  any  scale  even  temporarily. 

It  will  be  sufficient  to  fix  the  two  following  ideas  of  tem- 
perature : 

(1)  Of  two  bodies  in  thermal  communication  (by  conduction 
or  radiation),  that  one  which  imparts  heat  to  the  other  is  at  the 
higher  temperature.     If  neither  gains  or  loses,  they  are  at  the 
same  temperature. 

(2)  There  are  certain  temperatures,  such  as  the  freezing  and 
boiling  points  of  water  at  atmospheric  pressure,  which  are  fixed 
and  can  be  identified.     We  may  assume  that  there  are  a  series 
of  such  fixed  temperatures,  natural  or  artificial,  which  may  be 
compared  to  a  scale  of  hardness  ;    and  we  may  say  that  the 
temperature  of  a  body  coincides  with  one  of  them,  or  is  higher 
than  one  and  lower  than  another.     We  may,  if  we  choose,  use 
the  air  thermometer  for  the  purpose;    but  in   such    case    the 
degrees  are  to  be  considered  as  fixed  points  and  not  as  units  of 
measurement. 

We  may,  however,  admit  that  a  true  scale  is  possible,  and 
that  temperature  may  enter  into  an  equation,  but  that  the  form 
of  the  function  remains  to  be  determined. 

To  give  a  concrete  meaning  to  the  characteristic  equation, 
we  may  refer  to  the  combined  law  of  Boyle  and  Gay  Lussac  for 
a  perfect  gas.  If  we  accept  for  the  moment  the  scale  of  the 
air  thermometer,  the  law  may  be  represented  by  the  equation 


in  which  R  is  a  constant,  a  is  the  coefficient  of  dilatation  of 


4  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

air,  and  /  is  the  temperature  by  the  air  thermometer  on  the  Cen- 
tigrade scale.     Transposing, 


This  is  the  characteristic  equation  for  a  perfect  gas  in  terms 
of/,  v,  and  /,  in  which  a  may  be  assumed  to  be  constant. 

The  value  of  a  is  very  nearly  -  .     Consequently,  if  we 
make  --[-/  =  273.7  +  /  =  T,  we  shall  have,  instead  of  (3), 


(4) 


The  letter  T  is  used  to  represent  what  is  sometimes  called 
the  absolute  temperature  of  the  air  thermometer  above  the 
absolute  zero. 

Now,  air  near  the  freezing  point  of  water  expands  -  of 
its  volume  at  freezing  for  each  degree  of  increase  of  tempera- 

ture, and  also  contracts  --  of   its  volume  for  each  degree 

2737 

below  freezing.  If  the  thermometer  be  formed  of  a  tube  of 
uniform  calibre,  and  the  space  between  freezing  and  boiling  be 
divided  into  one  hundred  parts,  and  if  the  division  be  continued 
to  the  closed  ends,  there  will  be  273.7  divisions  below  freezing, 
point.  The  degrees  may  be  numbered  beginning  at  the  closed 
end  ;  and  the  temperatures  on  such  scale  will  be  represented  by 

T=  273-7  +  '- 

Now,  any  equation  with  three  variables  may  be  represented 
by  a  geometrical  surface,  referred  to  co-ordinate  axes,  of  which 
surface  the  variables  are  the  co-ordinates.  In  the  case  of  a 
perfect  gas  which  conforms  to  the  equation 


THERMAL   CAPACITIES.  5 

the  surface  is  such  that  each  section  perpendicular  to  the  T  is 
a  rectangular  hyperbola  (Fig.  i). 

Returning  now  to  the  general  case, 
and  abstaining  from  adopting  any  spe- 
cific scale  of  temperature,  it  is  apparent: 
that  the  characteristic  equation  of  any 
substance  may  be  represented  by  a 
geometrical  surface  referred  to  co-ordi- 
nate axes,  since  the  equation  is  assumed 
to  contain  only  three  variables  ;  but  the  FlG-  '• 

surface  will  in  general  be  less  simple  in  form  than  that  repre- 
senting the  combined  law  of  Boyle  and  Gay  Lussac. 

If  one  of  the  variables,  as  /,  is  given  a  special  constant  value, 
it  is  equivalent  to  taking  a  section  perpendicular  to  the  axis  of 
t ;  and  a  plane  curve  will  be  cut  from  the  surface,  which  may 
be  conveniently  projected  on  the  (/,  v)  plane. 

Sections  may  be  taken  perpendicular  to  the  other  axes,  and 
a  sufficient  number  of  such  sections,  or,  as  a  substitute,  the  pro- 
jections of  the  intersections,  will  give  a  complete  description  of 
the  surface.  The  whole  process  is  equivalent  to  a  complete 
solution  of  the  characteristic  equation,  but  there  are  few  sub- 
stances of  which  the  properties  are  sufficiently  well  known  for 
the  purpose. 

Other  curves  in  addition  to  the  sections  may  be  drawn  on 
the  surface  and  projected  on  the  (/,  v)  plane.  It  is  essential 
sometimes  to  distinguish  between  the  actual  curve  and  its  pro- 
jection. The  reason  for  choosing  the  (/,  v)  plane  is  that  the 
curves  drawn  correspond  to  those  drawn  by  the  indicator. 

Thermal  Capacities. — The  amount  of  heat  required  to 
change  by  unity  any  quality  of  a  unit  of  weight  of  any  body 
under  given  circumstances  is  called  the  thermal  capacity  corre- 
sponding to  the  given  change. 

In  three  cases  only  have  these  capacities  received  special 
names ;  i.e.,  specific  heat  at  constant  volume,  specific  heat  at 
constant  pressure,  and  latent  heat  of  expansion. 

Thermal  Unit. — Heat  is  measured  in  calories,  or  British 
thermal  units  (B.  T.  U.).  A  calorie  commonly  is  defined  as  the 


6  THERMODYNAMICS  OF   THE  STEAM-ENGINE. 

heat  required  to  raise  one  kilogram  of  water  from  freezing" 
point  to  one  degree  Centigrade  ;  and  a  British  thermal  unit, 
that  required  to  raise  one  pound  from  32°  to  33°  Fahrenheit. 
In  our  work,  for  reasons  that  will  appear  in  the  discussion  of 
the  specific  heat  of  water,  we  shall  choose  62°  F.  for  the  stand- 
ard temperature,  and  shall  define  a  B.  T.  U.as  the  heat  required 
to  raise  a  pound  of  water  from  62°  to  63°  F. 

This  statement  is  subject  to  the  same  indefiniteness  as  the 
thermal  scale  from  which  it  is  derived.  The  true  value  can  be 
defined  only  after  a  logical  thermal  scale  is  developed. 

Specific  Heat  is  the  heat  required  to  raise  one  unit  of 
weight  of  a  substance  through  one  degree  of  temperature, 
measured  in  thermal  units.  The  specific  heat  of  water  at  the 
standard  temperature  is  consequently  unity.  Two  specific 
heats  are  commonly  distinguished  ;  at  constant  pressure  Cp  ,  and 
constant  volume  cv  .  Both  of  these  specific  heats  are  liable  to 
be  variable  ;  consequently,  if  the  amount  of  heat  dQ  imparted 
to  a  unit  of  weight  of  a  substance  changes  the  temperature  by 

dt,  then  the  specific  heat  at  a  given  temperature  /  is  c  =  -^. 

If  the  change  takes  place  at  constant  pressure  or  at  constant 
volume,  then 


dQ\ 

jf  constant,  \&*JV  constant. 


or 

V 


Latent  Heat  of  Expansion  is  the  amount  of  heat  required 
to  change  the  volume  of  one  unit  of  weight  by  the  amount  of 
one  unit. 

As  this  prqperty  is  also  sometimes  variable,  we  may  prop- 
erly write  for  the  latent  heat  of  expansion  at  the  temperature  /, 


t  constant. 


General  Equations  of  the  Effects  produced  by  Heat— 

The  heat  given  to  a  body  and  which  produces  a  certain  change 


THERMAL    CAPACITIES, 


in  that  body  may  be  a  function  of  /,  v,  and  /.     If  v  and  t  are 
chosen  for  the  independent  variables,  then 


In  like  manner,  with  /  and  t  as  independent  variables, 

'  .....  (6a) 

and  with/  and  v  as  independent  variables, 


Substituting  for  (-7-)    >  in  equation  (5a),  the  specific  heat  at 

constant  volume,  and  for  (-7-)  ,  the  latent  heat  of  expansion, 

\av  It 

dQ  =  cvdt  +  ldv (5) 

In  like  manner  the  specific  heat  at  constant  pressure  may 
be  substituted  for  f-jr]  in  equation  (6a);  and  for  ("Trj    rnay  be 


substituted^  which  represents  the  amount  of  heat  required  to 
be  added  when  the  external  pressure  is  increased  by  unity,  a 
thermal  capacity  which  has  not  as  yet  received  a  name ; 
whence 

dQ  —  cpdt  +  mdp.    ......     (6) 

Finally,  rjrr]    may  be  represented  by  #,   and  Mr)    by  o, 

both  being  thermal  capacities  without  names,  and  equation  (/a) 
becomes 

dQ  —  ndp  +  odv (7) 

Relations  of  the  Thermal  Capacities. — The  three  equa- 
tions, (5),  (6),  and  (7),  show  the  changes  produced  by  the  addi- 


8  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

tion  of  an  amount  of  heat  dQ  to  a  unit  of  weight  of  a  substance, 
the  difference  coming  from  the  methods  of  analyzing  the 
changes,  but  the  total  amount  dQ  may  be  the  same  in  all  ;  con- 
sequently the  left-hand  members  maybe  equated,  forming  three 
equations.  Thus,  equating  (5)  and  (6), 


Idv  =  cpdt  +  mdp  ......     (&) 

. 

From  the  general  characteristic  equation  we  have 


from  which,  by  differentiating,  we  have 


which  substituted  in  (8)  gives 

dt 


...  c#  +  mdp  .  [c,,  +  ldt  +  l}dP.    .     .     (9) 

In  equation  (9)  /  and  /  are  independent  variables,  and  each 
may  have  all  possible  values;  consequently  we  may  equate  like 
coefficients. 


.-.    c>  =  cv  +  /(^-J  , (10) 

'©,=  «-"•'• "" 

Again,  equating  the  remaining  coefficients, 


In  like  manner,  by  differentiating  the  general  equation, 


THERMAL   CAPACITIES. 
which  substituted  in  (8)  gives 


)  *+&),*]=  **+**< 


Equating  like  coefficients, 


Equating  coefficients  of  dv, 


Finally,  equating  (5)  and  (7), 

cvdt  -\-  Idv  =  ndp  -\-  odv. 
Substituting  for  the  value  of  dt,  as  above, 


v\    dp  +  Idv  =  ndp  +  odv. 

\ap)v 


or 

Equating  (6)  and  (7), 

Cpdt  -f-  mdp  =  ndp  -f-  odv. 
Substituting  from 


10  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Equating  coefficients  of  dp, 

,dt 


tat  \ 
n  —  cJ-y-\ 

WJ: 


(18) 


In  the  preceding  work  we  have  six  coefficients.,  Cp,  cv,  /, 

m,  n,  and  o,  of  which  cp   is  commonly  known  for  any  substance. 

The  coefficient  cv  cannot  be  -readily  determined  directly,  but 

the  ratio  — -  =  K  is  known  for  so*pe  substances,  especially  gases, 

and  from  it  cv  may  be  found.  The  other  four  are  expressed  in 
terms  of  the  specific  heats,  which  for  convenience  are  here 
assembled  : 

dv 


ldt\ 
n  =  cv\-j-\    , 

\Opjm 


dt 

o  = 


m  = 


Also  we  have  in  general  for  three  variables,  as/,  z/,  and  t, 

dv\       dt 


also, 


The  relations  thus  far  deduced  are  merely  necessary  alge- 
braic relations  of  the  literal  functions,  and  are  related  to  the 
theory  of  heat  since  the  forms  are  those  that  appear  in  that 
theory.  They  are  theref6re  true,  whatever  theory  be  accepted 
and  whatever  scale  of  temperature  be  adopted. 


CHAPTER   II. 

FIRST   LAW   OF    THERMODYNAMICS. 

THE  formal  statement  of  the  first  law  of  thermodynamics  is: 
Heat  and  mechanical  energy  are  mutually  convertible,  and 
heat  requires  for  its  production  and  produces  by  its  disappearance 
a  definite  number  of  units  of  work  for  each  thermal  unit. 

The  mechanical  equivalent  of  heat  is  designated  by./,  and 
the  reciprocal  by  A  ;*  so  that 


(21) 


The  value  of  the  mechanical  equivalent  of  heat  given  by 
Joule,  and  long  quoted  in  all  works  on  heat,  is  77^  foot-pounds 
for  one  B.T.U.  In  the  French  system  the  equivalent  of  one 
calorie,  corresponding,  is  taken  to  be  424  meter-kilograms. 

The  value  of  J  determined  by  Rowland  at  62°  F.  or 
i6|°  C.  and  reduced  to  45°  of  latitude,  ist  for 

i  B.T.U.,  778  foot-pounds  ; 

i  calorie,  426.9  meter-kilograms  ; 

and  these  values  will  be  used  in  our  work  unless  the  contrary 
is  stipulated. 

This  law  is  a  special  statement  of  the  general  law  that 
energy  can  neither  be  created  nor  destroyed,  but  may  be  trans- 
muted from  one  form  to  another,  with  a  definite  number  of 
units  in  one  form,  equivalent  to  a  given  number  in  the  other. 
The  law  is  a  physical  and  experimental  law,  differing  essentially 
from  an  axiom. 

Effects  of  the  Transfer  of  Heat.  —  Let  a  quantity  of  any 
substance  of  which  the  weight  is  one  unit,  i.e.,  one  pound  or 
one  kilogram;  receive  a  quantity  of  heat  dQ.  It  will,  in  general, 
experience  three  changes,  each  requiring  an  expenditure  of 

ii 


12  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

energy.  They  are  :  (i)  The  temperature  will  be  raised,  and,  by 
the  theory  that  sensible  heat  is  due  to  the  vibrations  of  the 
particles  of  the  body,  the  kinetic  energy  will  be  increased.  Let 
dS  represent  this  change  of  sensible  heat  or  vibration  work  in 
units  of  work.  (2)  The  mean  positions  of  the  particles  will  be 
changed  ;  in  general  the  body  will  expand.  Let  dl  represent 
the  units  of  work  required  for  this  change  of  internal  potential 
energy,  or  work  of  disgregation.  (3)  The  expansion  indicated 
in  (2)  is  generally  against  an  external  pressure,  and  to  overcome 
the  same,  that  is,  for  the  change  in  external  potential  energy, 
there  will  be  required  the  work  dW. 

If  during  the  transmission  no  heat  is  lost,  and  if  no  heat  is 
transformed  into  other  forms  of  energy,  such  as  sound,  elec- 
tricity, etc.,  then  the  first  law  of  thermodynamics  gives 


(22) 

It  is  to  be  understood  that  any  or  all  of  the  terms  of  the 
equation  may  become  zero  or  may  be  negative.  If  all  the 
terms  become  negative,  heat  is  withdrawn  instead  of  added, 
and  dQ  is  negative.  It  is  not  easy  to  distinguish  between  the 
vibration  work  and  the  disgregation  work,  and  for  many  pur- 
poses it  is  unnecessary  ;  consequently  they  are  treated  together 
under  the  name  of  intrinsic  energy,  and  we  have 

dQ  =  A(dS+dI+dW)  =  A(dE+dW).  .,  .     (23) 

The  inner  work,  or  intrinsic  energy,  depends  on  the  state  of 
the  body,  and  not  at  all  on  the  manner  by  which  it  arrived  at 
that  state  ;  just  as  the  total  energy  of  a  falling  body,  with  refer- 
ence to  a  given  plane  consisting  of  kinetic  energy  and  potential 
energy,  depends  on  the  velocity  of  the  body  and  the  height 
above  the  plane,  and  not  on  the  previous  history  of  the  body. 

The  external  work  is  assumed  to  be  done  against  a  fluid 
pressure  ;  consequently 

...     (24) 


W=         pdv,     ......     (25) 

t/Z'O 

where  v  and  i\  are  the  final  and  initial  volumes. 


FIRST  LAW  OF   THERMODYNAMICS.  13 

This  assumption  holds  good  when  the  substance  itself  is  a 
fluid  ;  for  example,  the  steam  in  the  cylinder  of  an  engine. 

In  order  to  find  the  value  of  the  integral  v,  in  equation  (25), 
it  is  necessary  to  know  the  manner  in  which  the  pressure  varies 
with  the  volume. 

Since  the  pressure  may  vary  in  different  ways,  the  external 
work  cannot  be  determined  from  the  initial  and  final  states  of 
the  body.  The  heat  required  to  effect  a  change  from  one  state 
to  another  depends  on  how  the  change  is  effected. 

Assuming  the  law  of  the  variation  of  the  pressure  and  volume 
to  be  known,  we  may  integrate  thus  : 


(26) 


In  order  to  determine  E  for  any  state  of  a  body,  it  would 
be  necessary  to  deprive  it  entirely  of  vibration  and  disgregation 
energy,  which  of  course  involves  reducing  it  to  a  state  of  ab- 
solute cold.  Consequently  the  direct  determination  is  impossi- 
ble. However,  in  all  our  work  the  substances  operated  on  are 
changed  from  one  state  to  another,  and  in  each  state  the  intrin- 
sic energy  depends  on  the  state  only  ;  consequently  the  change 
of  intrinsic  energy  may  be  determined  from  the  initial  and  final 
states  only,  without  knowing  the  manner  of  change  from  one  to 
the  other. 

All  succeeding  equations  will  be  arranged  to  involve  differ- 
ences of  energy  only,  and  the  hypothesis  involved  in  a  separa- 
tion into  vibration  and  disgregation  work  avoided. 

Thermal  Lines.  —  The  external  work  can  be  determined 
only  when  the  relations  of  /  and  v  are  known,  or,  in  general, 
when  the  characteristic  equation  is  known.  It  has  already  been 
shown  that  in  such  case  the  equation  may  be  represented  by  a 
geometrical  surface,  on  which  so-called  thermal  lines  can  be 
drawn  representing  the  properties  of  the  substance  under  con- 
sideration. These  lines  are  commonly  projected  on  the  (/,  v) 
plane.  It  is  convenient  in  many  cases  to  find  the  relation  of  p 
and  v  under  a  given  condition  and  represent  it  by  a  curve  drawn 
directly  on  the  (p,  v)  plane. 


14  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

A  number  of  the  thermal  lines  will  be  thus  represented  and 
discussed. 

Isopiestic  lines,  or  lines  of  equal  pressure. — The 
change  of  condition  takes  place  at  constant  press- 
ure, and  consists  of  a  change  of  volume,  as  repre- 
sented in  Fig.  2.  The  tracing  point  moves  from 


FlG- 2-  a0  to  ajt  and  the  volume  changes  from  v0  to  vr 
The  work  done  is  represented  by  the  rectangular  area  under 
a,alt  or  by 


W 


=  P  I    ldv=p(vl  —  VQ). 

t/Z'O 


Durinff  the  change  the  temperature  may  or  may  not  change  ; 
the  diagram  shows  nothing  concerning  it. 

Isometric  lines,  or  lines  of  equal  volume. — The 
pressure  increases  at  constant  volume,  and  the 
tracing  point  moves  from  a0  to  ar  The  tempera- 
ture usually  increases  meanwhile.  Since  dv  is  zero, 


FIG.  3. 


W 


—   I    pd®  =  o. 

e/Z'o 


Isothermal  lines,  or  lines  of  equal  temperature. — The  tem- 
perature remains  constant,  and  a  line  is  drawn,  usually  convex, 
toward  the  axis  OV.  The  pressure  of  a  mixture  of  a  liquid  and 
its  vapor  is  constant  for  a  given  temperature  ;  consequently  the 
isothermal  for  such  a  mixture  is  a  line  of  equal  pressure,  repre- 
sented by  Fig.  2.  The  isothermal  of  a  perfect 
gas,  on  the  other  hand,  is  an  equilateral  hyper- 
bola, as  appears  from  the  law  of  Boyle,  which 
may  be  written 

FIG.  4.  pv—C (27) 

Isodynamic  or  isoenergic  lines  are  lines  representing  changes 
during  which  the  intrinsic  energy  remains  constant.  Conse- 
quently all  the  heat  received  is  transformed  into  external  work. 
It  will  be  seen  later  that  the  isodynam-ic  and  isothermal  linest 
for  a  gas  are  the  same. 


FIXST  LAW  OF    THERMODYNAMICS.  15 

Adiabatic  Lines.  —  A  very  important  problem  in  thermody- 
namics is  to  determine  the  behavior  of  a  body  when  change  of 
condition  occurs  without  gain  or  loss  of  heat  ;  that  is,  such  a 
change  as  would  occur  in  a  perfectly  non-conducting  vessel. 
During  the  change  heat  may  be  transformed  into  work,  or  vice 
versa  ;  but  no  heat  is  transferred  in  the  form  of  heat.  Direct 
experiments  are  very  difficult,  and  are  usually  approximations  ; 
very  rapid  changes  in  any  vessel  are  nearly  adiabatic,  since  time 
is  required  for  conduction  and  radiation  of  heat.  Rankine  gave 
the  name  adiabatic  to  lines  representing  the  volume  and  press- 
ure during  changes  that  occur  without  transmission  of  heat. 
When  there  is  no  transmission  of  heat,  equation  (26)  becomes 


o  =  Q  =  A  E,  - 
consequently, 

-  (£,  -  £,)  =         pdv,    ......    (28) 


which  shows  that  work  done  by  the  body  against  external, 
pressure  is  at  the  expense  of  the  intrinsic  energy.  Since  the 
two  quantities  are  numerically  equal,  the  sign  may  frequently 
be  neglected  in  numerical  problems. 

When  an  adiabatic  crosses  an  isothermal,  both  being  pro- 
jected on  the  (/,  v)  plane,  it  is  the  steeper,  as  shown  at  a0  , 
Fig.  5.  This  is  easily  shown  for  substances  that 
expand  with  the  rise  of  temperature.  For,  if  a 
body  expands  in  a  non-conducting  vessel,  the 
external  work  done  is  at  the  expense  of  the  in- 
trinsic energy,  as  shown  by  equation  (28)  ;  and  a 
diminution  of  the  intrinsic  energy  in  general  is  FIG.  5. 

made  up  of  a  loss  of  potential  energy,  due  to  molecular  ar- 
rangement, and  a  loss  of  kinetic  energy,  due  to  temperature. 

Now,  a  loss  of  temperature  at  constant  pressure  causes  a 
contraction  of  volume  ;  or,  conversely,  at  constant  volume  a 
loss  of  temperature  causes  a  lowering  of  pressure.  In  Fig.  5 
an  expansion  at  constant  temperature  is  represented  by  the 
isothermal  a9aiy  while  an  expansion  without  transmission  of  heat 


1 6  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

is  represented  by  the  adiabatic  a0a' '.  The  final  volume  is  the 
same  ;  consequently  the  pressure  represented  by  a'  is  less,  since 
the  adiabatic  expansion  is  accompanied  by  a  loss  of  temperature. 
Graphical  Representations  of  Change  of  Intrinsic 
Energy. — Professor  Rankine  first  used  a  graphical  method  of 
representing  a  change  of  intrinsic  energy,  employing  adiabatic 
lines  only,  as  follows  : 

Suppose  that  a  substance  is  originally  in  the  state  A  (Fig. 
6),  and  that  it  expands  adiabatically ;  then  the  external  work 
is  done  at  the  expense  of  the  intrinsic  en- 
ergy ;  hence,  if  the  expansion  has  proceeded 
to  A  i ,  the  area  AA^a^a,  which  represents  the 
external  work,  also  represents  the  change  of 
intrinsic  energy.     Suppose  that  the  expan- 
a        o7~^    sion  were  to  continue  indefinitely  ;  then  the 
FlG-6-  adiabatic  will  approach  the  axis  OV  indefi- 

nitely, and  the  area  representing  the  work  will  be  included 
between  the  curve  Aa  produced  indefinitely,  the  ordinate  Aa, 
and  the  axis  OV\  this  area  will  represent  all  the  work  that  can 
be  obtained  by  the  expansion  of  the  substance ;  and  if  it  be 
admitted  that  during  the  expansion  all  the  intrinsic  energy  is 
transformed  into  work,  so  that  at  the  end  the  intrinsic  energy 
is  zero,  it  represents  also  the  intrinsic  energy.  In  cases  for  which 
the  equation  of  the  adiabatic  can  be  found,  it  is  easy  to  show 
that 


is  a  finite  quantity ;  and  in  any  case,  if  we  admit  an  absolute 
zero  of  temperature,  it  is  evident  that  the  intrinsic  energy  can- 
not be  infinite.  On  the  other  hand,  if  an  isothermal  curve  were 
treated  in  the  same  way,  the  area  would  be  infinite,  since  heat 
would  be  continually  added  during  the  expansion. 

Now  suppose  the  body  to  pass  from  the  condition  repre- 
sented by  A  to  that  represented  by  B,  by  any  path  whatever ; 
that  is,  by  any  succession  of  changes  whatever ;  for  example, 
that  represented  by  the  irregular  curve  AB.  The  intrinsic 
energy  in  the  state  B  is  represented  by  the  area  VbBfi.  The 


FIXST  LAW  OF   THERMODYNAMICS. 


FIG.  7. 


change  of  intrinsic  energy  is  represented  by  the  area  fiBbaAa, 
and  this  area  does  not  depend  on  the  form  of  the  curve  AB. 
This  graphical  process  is  only  another  way  of  stating  that  the 
intrinsic  energy  depends  on  the  state  of  the  substance  only,  and 
that  change  of  intrinsic  energy  depends  on  the  final  and  initial 
states  only. 

Another  way  of  representing  change  of  intrinsic  energy  by 
aid  of  isodynamic  lines  avoids  an  infinite  diagram.  Suppose 
the  change  of  state  to  be  represented  by  the  p 
,curve  AB,  Fig.  7.  Draw  an  isodynamic  line 
AC  through  the  point  A,  and  an  adiabatic 
line  BC  through  B,  intersecting  at  C.  Then 
the  area  ABba  represents  the  external  work, 
and  the  area  bBCc  represents  the  change  of 
intrinsic  energy ;  for  if  the  body  be  allowed 
to  expand  adiabatically  till  the  intrinsic  energy  is  reduced  to  its 
original  amount  at  the  condition  represented  by  A,  the  external 
work  bBCc  will  be  done  at  the  expense  of  the  intrinsic  energy. 
Since  the  intrinsic  energy  is  constant  for  all  points  on  the 
isodynamic  line  through  A,  and  in  like  manner  is  constant  for 
points  on  the  line  through  B,  there  will  be  the  same  change  of 
intrinsic  energy  in  passing  from  a  condition  represented  by  any 
point  of  the  line  through  A  to  any  point  of  the  line  through  B ; 
consequently,  if  through  any  point,  as  D  of  the  upper  line,  an 
adiabatic  DE  be  drawn,  the  area  dDEe  will  be  equal  to  bBCc, 
and  will  equally  represent  the  change  of  intrinsic  energy  from 
the  point  A  to  the  point  B. 

Entropy. — If  a  body  have  its  condition  represented  by  the 
point  e  of  the  isothermal  aal  (Fig.  8),  it  will  have  a  definite 
temperature,  which  will  be  the  same  so  long  as 
its  condition  is  represented  by  some  point  on 
aal ,  as,  for  example,  al ,  though  the  volume  and 
pressure  will  meanwhile  have  varied.  Should 
the  temperature  change,  the  condition  will  be 
represented  by  some  point,  as  /,  on  another 
isothermal  bbl .  There  will  evidently  be  the 
same  change  of  temperature  in  passing  from  e  to  f  as  from 


FIG.  8. 


1 8  THERMODYNAMICS  OF   THE   STEAM-ENGINE, 

to/, ;  that  the  changes  of  volume  and  pressure,  external  work, 
and  intrinsic  energy  are  different  does  not  affect  the  statement 
concerning  the  temperature.  In  like  manner,  it  is  indifferent 
how  or  at  what  part  of  the  diagram  the  transfer  from  bbl  to  cct 
is  accomplished ;  the  same  change  of  temperature  must  occur. 
Let  aal ,  bbl ,  and  ccl  represent  adiabatic  lines. 
Then  if  a  body  having  its  condition  represented 
by  a  point  on  aal  experience  a  change  repre- 
sented by  eel ,  it  will  have  neither  lost  nor  gained 
heat  as  such,  though  heat  may  have  been 
changed  into  work ;  or,  vice  versa,  any  change 
that  can  be  represented  by  a  portion  of  an  adia- 
batic line  will  be  subject  to  the  same  condition.  There  is, 
we  see,  some  property  of  the  body  that  remains  constant 
during  an.  adiabatic  change ;  and  that  property  is  called  the 
entropy.  If  the  substance  has  its  condition  represented  by/, 
it  will  have  a  different  entropy  ;  but  for  any  change  represented 
by  a  portion  of  the  lin«  bb^ ,  as  ffl ,  the  entropy  will  be  constant. 
Just  as  a  change  involving  the  passage  from  one  isothermal  to 
another  requires  a  definite  change  of  temperature,  so  a  change 
involving  the  passage  from  one  adiabatic  to  another  involves  a 
definite  change  of  entropy.  Thus  a  passage  from  e  to  /  involves 
the  same  change  of  entropy  as  a  change  from  <?,  to/  ;  again, 
the  path  from  e  to  /  is  indifferent,  and  has  purposely  been  rep- 
resented as  irregular. 

That  the  passage  from  one  adiabatic  to  another  under  dif- 
ferent circumstances  may  involve  different  changes  of  volume 
and  pressure,  external  work,  etc.,  does  not  affect  the  statement 
concerning  the  entropy.  * 

An  expression  for  the  entropy,  as  for  the  different  thermal 
capacities,  can  be  found  in  some  cases.  Entropy  will  be  repre- 
sented by  0.  It  is  a  property  of  a  body  similar  to  specific 
volume,  specific  heat,  and  latent  heat  of  expansion,  but  most 
nearly  akin  to  temperature.  It  depends  on  the  state  of  the 
body  and  not  on  the  method  of  the  change. 


CHAPTER  III. 

SECOND   LAW   OF  THERMODYNAMICS. 

Heat  Engines  are  engines  by  which  heat  is  transformed 
into  work.  All  actual  engines  used  as  motors  go  through  con- 
tinuous cycles  of  operations,  which  periodically  return  things 
to  the  original  conditions.  All  heat-engines  are  similar,  in  that 
they  receive  heat  from  some  source,  transform  part  of  it  into 
work,  and  deliver  the  remainder  (minus  certain  losses)  to  a 
refrigerator. 

The  source  and  refrigerator  of  a  condensing  steam-engine 
are  the  furnace  and  the  condenser.  The  boiler  is  properly  con- 
sidered as  a  part  of  the  engine,  and  receives  heat  from  the 
source. 

Carnot's  Engine. — :It  is  convenient  to  discuss  a  simple 
ideal  engine,  first  described  by  Carnot ;  though,  from  a  defect 
in  the  theory  of  heat  then  accepted,  his  description  was 
erroneous. 

Let  P  of  Fig.  10  represent  a  cylinder  with  non-conducting 
walls,  in  which  is  fitted  a  piston,  also  of  non-conducting  mate- 
rial, and  moving  without  friction  ;  on 
the  other  hand,  the  bottom  of  the 
cylinder  is  supposed  to  be  of  a  material 
that  is  a  perfect  conductor,  and  which 
has  a  zero  thermal  capacity.  There  is 
a  non-conducting  stand  C  on  which  the 
cylinder  can  be  placed  while  adiabatic 
changes  take  place.  The  source  of  heat  A  at  a  temperature  / 
is  supposed  to  be  so  maintained  that  in  operations  during  which 
the  cylinder  is  placed  on  it,  and  draws  heat  from  it,  the  tem- 
perature is  unchanged.  The  refrigerator  B  at  the  temperature 
*,in  like  manner  can  withdraw  heat  from  the  cylinder  when  it 
is  placed  on  it,  at  a  constant  temperature. 

19 


* 


2O  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Let  there  be  a  unit  of  weight  (for  example,  one  pound)  of 
a  certain  substance  in  the  cylinder  at  the  temperature  t  of  the 
source  of  heat.  Place  the  cylinder  on  the  source  of  heat  A 
(Fig.  10),  and  let  the  substance  expand  at  the  constant  tem- 
perature /,  receiving  heat  from  the  source  A. 

If  the  first  condition  of  the  substance  be 
represented  by  A  (Fig.  1 1),  then  the  second 
will  be  represented  by  B,  and  AB  will  be  an 
isothermal.  If  Ea  and  Eb  are  the  intrinsic 
energies  at  A  and  B,  and  if  Wab ,  represented 
by  the  area  aABb,  be  the  external  work,  the 


FIG.  ii. 

1 


heat  received  from  A  will  be 


^aab. 

Now  place  the  cylinder  on  the  stand  C  (Fig.  10),  and  let 
the  substance  expand  adiabatically  until  the  temperature  is  re- 
duced to  /,  ,  that  of  the  refrigerator,  the  change  being  repre- 
sented by  the  adiabatic  BC  (Fig.  11).  If  Ec  is  the  intrinsic 
energy  at  C,  then,  since  no  heat  passes  into  or  out  of  the  cylinder, 


where  Wbc  is-  the  external  work  represented  by  the  area  bBCc. 
Place  the  cylinder  on  the  refrigerator  B,  and  compress  the  sub- 
stance till  it  passes  through  the  change  represented  by  CD, 
yielding  heat  to  the  refrigerator  so  that  the  temperature  remains 
constant.  If  Ed  is  the  intrinsic  energy  at  D,  then 

-Ql  =  A(Ed-Ec-  Wcd) 

is  the  heat  yielded  to  the  refrigerator,  and  WC(i,  represented  by 
the  area  cCDd,  is  the  external  work,  which  has  a  minus  sign 
since  it  is  done  on  the  substances. 

The  point  D  is  determined  by  drawing  an  adiabatic  from  A 
to  intersect  an  isothermal  through  C.  The  process  is  com- 
pleted by  compressing  the  substance  while  the  cylinder  is  on 
the  stand  C  (Fig.  10)  till  temperature  rises  to  /,  the  change 


SECOND  LAW  OF   THERMODYNAMICS.  21 

being  represented  by  the  adiabatic  DA.     Since  there  is   no 
transfer  of  heat, 


Adding  together  the  several  equations,  member  to  member, 

Wte  -  Wcd-  Wda  ; 


or,  if  W  be  the  resulting  work  represented  by  the  area  ABCD, 
then 


that  is,  the  difference  between  the  heat  received  and  the  heat 
delivered  to  the  refrigerator  is  the  heat  transformed  into  work. 

Carnot,  in  his  description  of  the  engine,  gives  instruction  to 
compress  the  substance  during  the  third  operation,  and  while 
in  connection  with  the  refrigerator,  till  all  the  heat  received 
from  the  source  of  heat  is  yielded,  and  then  to  complete  the 
cycle  by  an  adiabatic  compression.  The  caloric  theory  of  heat, 
assuming  it  to  be  a  substance,  required  such  a  statement,  and 
Carnot  compared  the  difference  of  temperature  to  a  difference 
of  head  of  water  in  hydraulics.  In  the  description  now  common 
the  operation  of  the  engine  corresponds  to  the  first  law  of 
thermodynamics. 

A  Reversible  Engine  is  one  that  may  run  either  in  the 
usual  manner,  transforming  heat  into  work,  or  reversed,  describ- 
ing the  same  cycle  in  the  opposite  direction,  and  transforming 
work  into  heat. 

A  Reversible  Cycle  is  the  cycle  of  a  reversible  engine. 

Carnot's  engine  is  reversible,  the  reversed  cycle  being 
ADCBA  (Fig.  n),  during  which  work  is  done  by  the  engine  on 
the  working  substance.  The  engine  then  draws  from  the 
refrigerator  a  certain  quantity  of  heat,  it  transforms  a  certain 
quantity  of  work  into  heat,  and  delivers  the  sum  of  both  to  the 
source  of  heat. 


22 


THERMODYNAMICS  OF   THE   STEAM-EXG1NE. 


A  Closed^Cjccle  is  any  cycle  in  which  the  final  state  is  the 
same  as  the  initial  state.  Fig.  12  represents 
such  a  cycle  made  up  of  four  curves  of  any 
nature  whatever.  If  the  four  curves  are  of  two 
species  only,  as  in  the  diagram  representing  the 
cycle  of  Carnot's  engine,  the  cycle  is  said  to  be 
simple.  In  general,  we  shall  have  for  a  cycle 


FIG.  12. 


like  that  of  Fig.  12,  ' 


=  A 


FIG.  13. 


Wbc  -  Wcd-  Wda\ 

A  closed  curve  of  any  form  may  be  consid- 
ered to  be  the  general  form  of  a  closed  cycle  ; 
as  that  in  Fig.  13.  For  such  a  cycle  we  have 

/  dQ  =  A  I  dW,  which  is  one  more  way  of 

stating  the  first  law  of  thermodynamics. 

It  may  make  this  last  clearer  to  con- 
sider the  cycle  of  Fig.  14,  composed  of  the 
isothermals  AB,  CD,  and  EG,  and  the 
adiabatics  BC,  DE,  and  GA.  The  cycle 
may  be  divided  by  drawing  the  curve 
through  from  C  to  F.  It  is  indifferent 
whether  the  path  followed  be  ABCDEGA 
or  ABCFCDEGA  or,  again,  ABCFGA  +  CDEFC. 

Again,  an  irregular  figure  may  be  imagined  to  be  cut  into 
elementary  areas  by  isothermals  and  adia- 
batic  lines,  as  in  Fig.  15.  The  summation 
of  the  areas  will  give  the  entire  area,  and 
the  summation  of  the  works  represented 
by  these  will  give  the  entire  work  repre- 
sented  by  the  entire  area. 

The  Efficiency  of   an  engine  is  the 


FIG.  14. 


FIG.  15. 


ratio  of  the  heat  changed  into  work  to  the  entire  heat  applied  ; 
so  that  if  it  be  represented  by  77, 


AW 
-Q-. 


(29) 


SECOND  LAW  OF   THERMODYNAMICS.  2$ 

Carnot  enunciated  a  principle  which  may  be  stated  as 
follows  : 

Carnot  's  Principle.  —  Of  all  engines  working  between  the 
same  source  of  heat  and  the  same  refrigerator,  a  reversible  engine 
gives  the  maximum  efficiency. 

For,  suppose  there  are  two  engines,  one  A,  of  any  kind 
whatever,  and  one  R,  which  is  reversible,  and,  for  simplicity, 
let  each  take  the  same  quantity  of  heat  Q  from  the  source  of 
heat  per  unit  of  time  while  running  direct.  The  engine  R,  if 
reversed,  will  deliver  the  same  quantity  Q  of  heat  per  unit  of 
time  to  the  source.  Now,  if  the  efficiency  of  A  is  greater  than 
that  of  R,  that  is,  if 


r 
>  —Q-,     or     Wa  >  Wr, 


then  A,  coupled  with  R,  will  be  able  to  run  R  reversed,  and  at 
the  same  time  produce  available  work  equal  to  Wa  —  Wr. 

This  surplus  work  can  come  from  the  refrigerator  only,  since 
the  heat  taken  from  the  source  of  heat,  and  the  heat  returned 
to  it,  in  a  unit  of  time  are  equal.  But  experience  and  experi- 
ment show  that  work  cannot  be  so  done.  Moreover,  if  it  be 
admitted  that  surplus  work  can  be  done  at  the  expense  of  the 
refrigerator,  the  admission  involves  the  ultimate  conclusion  that 
by  such  a  process  all  the  heat  might  be  abstracted  from  the 
refrigerator.  In  general,  the  efficiency  of  a  non-reversible 
engine  is  less  than  that  of  a  reversible  engine.  But  there  is  no 
fundamental  reason  why  it  may  not  approach  the  efficiency  of 
a  reversible  engine,  or  become  equal  to  it. 

The  Second  Law  of  Thermodynamics  is  a  formal  state- 
ment of  Carnot's  principle.  It  is  variously  stated,  but  each 
statement  involves  the  same  principle,  which  may  be  considered 
to  be  an  experimental  law. 

(1)  All  reversible  engines,  working  between  the  same  source  of 
heat  and  refrigerator,  have  the  same  efficiency;  i.e.,  the  efficiency 
is  independent  of  the  working  material. 

(2)  A  self-acting  machine  cannot  convey  heat  from  one  body  to 


24  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

another  at  a  higher  temperature.  This  is  almost  equivalent  to 
the  convention,  that  of  two  bodies,  the  one  to  which  heat  passes 
by  conduction  or  radiation  has  the  lower  temperature. 

Carnot's  Function. — Taking  Carnot's  principle,  that  the 
efficiency  of  a  reversible  engine  is  independent  of  the  working 
substance,  we  thereby  eliminate  from  the  expression  for  the 
efficiency  the  variables  /  and  v,  the  specific  pressure  and  the 
specific  volume,  since  they  are  properties  of  the  working  sub- 
stance. The  efficiency,  therefore,  depends  only  on  the  tem- 
perature of  the  source  of  heat,  and  the  difference  between  that 
temperature  and  the  temperature  of  the  refrigerator.  This 
statement,  in  the  form  of  an  equation,  is 


in  which  Q  is  the  heat  received,  and  Q  that  rejected  by  the 
engine,  and  t  and  t'  are  the  temperatures  of  the  source  of  heat 
and  of  the  refrigerator,  on  a  scale  which  we  have  assumed  to  be 
possible  but,  as  yet,  undetermined. 

If  the  temperature  of  the  refrigerator  approaches  near  that 
of  the  source  of  heat,  Q  —  Q  and  t  —  t'  become  AQ  and  At, 
and  at  the  limit  dQ  and  dt,  so  that 


(31) 


But  dt  is  itself  a  function  of  /,  so  that  at  the  limit  the  effi- 
ciency depends  on  t  only. 

Multiplying  and  dividing  by  dt, 

dQ      F(t,dt)^ 


SECOND  LAW  OF   THERMODYNAMICS.  2$ 

and  considering  that  the  coefficient  of  dt  is  a  function  of  /only, 
equation  (31)  becomes 


(32) 


/(/)  is  called  Carnot's  function,  and  is  represented  by/*;  its 
form  will  depend  on  the  thermometric  scale  adopted.  Had 
any  scale  like  that  oi  the  mercurial  or  air  thermometer  been 
adopted,  it  would  now  be  necessary  to  investigate  the  form  of 
the  function,  which  would  be  more  or  less  complicated. 
f  Equation  (32)  is  commonly  written 


(33) 


Absolute  Scale  of  Temperature.  —  A  scale  of  temperature 
may  now  be  defined  by  making  /*  =  -~,,  so  that 


Q 


the  large  T  being  used  instead  of  /  to  avoid  confusion  with  the 
common  scales.  The  scale  depends  on  the  efficiency  of  the 
reversible  engine,  and  consequently  does  not  depend  on  the 
property  of  any  substance.  Since  the  reversible  engine  is 
purely  ideal,  the  absolute  scale  is  also  ideal  ;  but  the  corre- 
spondence between  it  and  the  scale  of  the  air  thermometer,  with 
which  it  agrees  very  closely,  can  and  has  been  determined  by 
indirect  methods.  The  scale  proposed  is  justified  by  the  sim- 
plicity it  introduces  into  thermodynamic  equations,  and  involves 
no  inconsistency. 

The  method  of  defining  temperature  just  stated  was  first 
proposed  by  Sir  William  Thomson  ;  and  the  thermometric  scale 
resulting  is  sometimes  called  Thomson's  absolute  scale.  He  also 
gives  a  graphical  representation  of  the  scale,  which  may  be  taken 
to  be  the  equivalent  of  the  work  establishing  Carnot's  function. 


26  THERMODYNAMICS  OF   THE  STEAM-ENGINE. 

In  Fig.   1 6,  let  ak  and  bi  be  two  adiabatic  lines,  and  let 
the  substance  have  its  condition  represented  by  the  point  a. 

Through  a  and  d  draw  iso- 
thermal lines,  then  the  dia- 
gram abed  represents  the  cycle 
of  a  simple  reversible  engine. 
Draw  the  isothermal  line  fe> 
so  that  the  area  dcef  shall  be 
equal  to  abcd\  then  the  dia- 
.  gram  dcef  re  presents  the  cycle 


FlG-  l6-  of  a  reversible  engine,  doing 

the  same  amount  of  work  per  stroke  as  that  engine  whose  cycle 
is  represented  by  abed ';  and  the  difference  between  the  heat 
drawn  from  the  source  and  delivered  to  the  refrigerator,  i.e.,  the 
heat  transformed  into  work,  is  the  same.  The  refrigerator  of 
the  first  engine  might  serve  for  the  source  of  heat  for  the 
second. 

Suppose  that  a  series  of  equal  areas  were  cut  off  by  isother- 
mal lines,  as /<?£•/*,  kgik,  etc.,  and  suppose  there  were  a  series  of 
reversible  engines  corresponding;  then  there  would  be  a  series 
of  sources  of  heat  of  determinate  temperatures,  which  might 
be  chosen  to  establish  a  thermometric  scale.  In  order  to  have 
the  scale  correspond  with,  those  of  ordinary  thermometers,  one 
of  the  sources  of  heat  should  be  at  the  temperature  of  boiling 
water,  and  one  at  that  of  melting  ice  ;  and  for  the  Centigrade  scale 
there  should  be  one  hundred,  and  for  the  Fahrenheit  scale  one 
hundred  and  eighty  such  cycles  with  the  appropriate  sources  of 
heat,  between  boiling  and  freezing  point.  To  establish  the  ab- 
solute zero  of  the  scale  the  series  must  be  imagined  to  be  con- 
tinued till  the  area  included  between  an  isothermal  and  the  two 
adiabatics,  continued  indefinitely,  shall  not  be  greater  than  one 
of  the  equal  areas. 

The  absolute  zero  thus  determined  is  very  nearly  identical 
with  that  of  the  air  thermometer;  and  for  all  engineering  pur- 
poses one  may  be  used  for  the  other. 

Scale  of  Entropy. — It  is  convenient  to  take  the  areas  of 
Fig.  1 6  to  represent  778  foot-pounds  when  the  Fahrenheit  scale 


SECOND  LA  W  OF   THERMOD  YNAMICS.  2/ 

is  used,  that  being  the  equivalent  of  one  thermal  unit.  Sup- 
pose further  that  a  second  adiabatic  be  drawn  through  b'c'e'g'i' , 
making  the  area  bb'c'c  equal  to  those  of  the  first  series  ;  then  the 
points  a,  b,  b ',  bfl ',  etc.,  if  a  series  of  adiabatics  be  drawn,  repre- 
sent the  conditions  of  the  working  substance  after  the  succes- 
sive addition  of  /  units  of  heat  at  constant  temperature  A  The 
adiabatics  may  be  numbered  0,  0  +  J>  0  +  2»  etc.,  to  0'. 

Each  one  of  the  areas  included  between  a  pair  of  isothermals 
and  a  pair  of  adiabatics  will  represent  the  mechanical  equivalent 
of  one  thermal  unit,  provided  abed  be  chosen  as  directed  above. 
The  proof  may  be  given  in  the  following  manner:  The  two 
areas,  dcef  and  bb'c'c,  are  equal  to  abed  by  construction.  The 
two  engines  working  on  the  cycles  abed  and  bb'c'c  each  draw 
the  same  quantity  of  heat  from  the  source  and  reject  the  same 
quantity  to  the  refrigerator;  for  they  transform  the  same 
quantity  of  heat  into  work  per  stroke,  and,  working  between 
the  same  temperatures,  they  have  the  same  efficiency.  The 
engines  working  on  the  cycles  dcef  and  cc'e'e  consequently  re- 
ceive the  same  amount  of  heat  per  stroke  from  their  sources  of 
heat ;  and,  since  they  work  between  the  same  temperatures, 
they  must  transform  the  same  amount  of  heat  into  work,  or 
what  is  the  same  thing,  the  area  cc'e'e  is  equal  to  dcef;  and 
further,  all  four  areas  are  equal.  In  the  same  way  the  proof 
may  be  extended  to  all  areas  laid  off  in  a  similar  method. 

A  perfect  engine  working  between  the  isothermals  T  and  Tf 
and  the  adiabatics  0  and  0'  will  change  into  work  per  stroke 
the  heat 


.    .    (35) 


in  which  equation  0  is  the  initial  entropy  of  the  working  sub- 
stance, and  0'  —  0  is  the  change  of  entropy  from  one  adiabatic 
to  the  other. 

Suppose  that  Tf  becomes  zero,  and  that  0'  —  0  becomes 
d(f>,  then 


28 


THERMODYNAMICS  OF  THE  STEAM-ENGINE. 


(36) 

(37) 


Efficiency  of  Reversible  Engines.—  The  efficiency  of  a 
reversible  engine  given  by  equation  (29)  may  be  written 


(38) 

But  the  integration  of  the  equation  (34)  between  limits  gives 
'  T 


(39) 


This  equation  may  also  be  derived  by 
the  graphical  method   used  in  discussing 
the    absolute    temperature.      In    Fig.    17 
let  ABCD  be  the  cycle  of  a  re- 
versible engine  working  between 
the  temperatures  T  and  T'  and 
the    entropies    0   and 
'  -f        </>'.     Let  intermediate 
isothermal    and    adia- 
batic   lines   be  drawn 

dividing  the  cycle  into  quadrilaterals  each  one  of  which  rep- 
resents 778  foot-pounds,  or  one  thermal  unit ;  then  it  is  appar- 
ent that  the  number  of  these  quadrilaterals  in  the  cycle,  and 
the  number  of  thermal  units  changed  into  work,  is 


FIG.  17. 


Similarly,    the   total   heat   absorbed   during   the  operation 
represented  by  AB  is 

T(4>'  -  <fi). 


SECOND  LAW  OF   THERMODYNAMICS.  2$ 

Consequently  the  efficiency  is 

_  AW      (T~T\<t>'  -0)  _  T-Tf 
**  =      Q  7X0'  -0)  T~ 

Alternative  Method.  —  The  method  of  developing  the  idea 
of  temperature  from  the  second  law  has  for  an  advantage  the 
fact  that  the  difficulty  of  giving  an  adequate  physical  defini- 
tion is  made  prominent.  Some  writers,  Zeuner,  Verdet,  and 
others,  prefer,  however,  to  avoid  the  difficulty  by  delaying 
the  discussion  of  temperature  ;  and  of  the  general  equations  (5), 
(6),  and  (7),  employ  only  the  latter, 

dQ  =  ndp  +  odv. 
Equation  (23)  may  be  written 


which,  combined  with  the  equation  above,  gives 
dE  d 

Differentiating, 


-f-A 

dp  ~* 


dvdP 

But  E  depends  on  the  state  only,  and  dE  is  an  exact  differ- 
ential ; 


dpdv      dv  dp' 


3O  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

and  by  subtraction  the  preceding  equations  give 


ldo\         idn\ 

y  -u  =' (40) 


\dplv       \dv)p 

Now  if  dQ  were  an  exact  differential,  §o  that  it  could  be 
integrated  directly,  as  would  be  the  case  if  Q  depended  on  the 
initial  and  final  states  only,  we  should  then  have 


~dpdv      dvdp' 
which  may  be  written 


Performing  this  operation  on  equation  (7)  would  give,  in 
such  case, 

ldo\   j     ldn\ 
\dp)v  ~  \dv>; 

A  comparison  of  this  last  equation  with  the  true  equation 
(40)  shows  that  dQ  is  not  an  exact  differential,  and  that  equa- 
tion (7)  cannot  be  integrated  directly. 

Suppose  now  that  -    is  an  integrating  factor,  such  that 


dQ      n 


may  be  integrated  directly.     The  adiabatic  equations 
0  —  const.,     0'  =  const.,     0"  =  const.,    etc., 


SECOND  LAW  OF   THERMODYNAMICS.  31 

represent  a  series  of  adiabatic  lines,  and  in  like  manner  the 
equations 

-  =  const.,     -~  =  const.,     -^77  =  const.,  etc., 

may  represent  a  series  of  thermal  lines. 

In  Fig.  1 8  let  the  cycle  A  BCD  be  com- 
posed of  the  adiabatic  lines  AD  and  C&,  and 
the  lines  AB  and  CD  represented  by  the 
equations 

T.  =  const,    and    -<=7  =  const. 


FIG.  18. 

A  reversible  engine,  receiving  the  heat  Q  per  stroke,  and 
rejecting  the  heat  Q',  will  have  the  efficiency 

_Q- Q  _AW 
*=    ~Q~       Q  ' 

But  -r-  is  an  exact  differential  depending  on  the  state  only, 
so  that  for  the  entire  cycle 


Now,  during  the  operations  represented  by  the  adiabatics 
AD  and  BC  no  heat  is  transmitted,  and  during  the  operations 

represented  by  the   lines  AB   and  CD,  -~  is  constant ;  conse- 
quently the  integration  for  the  cycle  gives 

Q_&- 

Q*  CV  > 

Q-Q     S-S' 


Q 


That  is,  the  efficiency  of  an  engine  working  on  such  a  cycle 
depends  on  5  and  S' ,  and  on  nothing  else. 


32  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Thus  far  temperature  has  not  been  brought  into  the  dis- 
cussion, and  it  may  be  defined  as  seems  fit.  Let  the  absolute 
temperature  be  defined  by  the  equation 

T=S; 
then  equation  (41)  becomes 

Q-  Q  __T-T' 

Q  T     ' 

so  that  the  absolute  temperature  depends  on  the  efficiency  of 
a  reversible  engine,  as  in  the  preceding  discussion  involving 
Carnot's  function. 

Generalization  of  Carnot's  Principle. — Carnot's  princi- 
ple, or  the  second  law  of  thermodynamics,  is  sometimes  stated 

dQ 

by  making  -~  an  exact  differential,  or  by  writing  for  a  reversi- 
ble cycle 

f -.     • (43) 


fdQ_ 
J    T~ 


This  is  immediately  evident  from  equation  (37),  since  0,  the 
entropy,  is  a  property  of  the  substance  and  depends  on  the  state 
only.  Now  in  a  reversible  cycle  the  substance  is  in  the  same 
state  at  the  end  as  at  the  beginning  of  the  cycle ;  consequently 
if  d(J>  be  integrated  and  the  limits  used  are  those  at  the  begin- 
ning and  end  of  the  cycle,  that  is,  are  identical,  the  integral 

will  be  equal  to  zero.     At  the  same  time  -=  will  give  zero  for 

its  integral  between  the  same  limits.  This  may  be  represented 
graphically  as  follows : 

Let  ABCDEFGA,  Fig.  19,  represent  a  cycle  composed  of 
isothermals  and  adiabatics  ;  then  it  may  be  divided  by  CE  into 
two  simple  cycles. 

For  the  cycle  ABCFGA  we  have 

Q 


SECOND  LAW  OF   THERMODYNAMICS. 


33 


whence 


QL=^.  .  0i=0.  .  Q  _&_= 


Q  being  the  heat  absorbed  at  the  temperature  T  along  the  path 
AB,  and  Q  the  heat  rejected  at  the  temperature  T'  along  the 
path  FG. 

In  like  manner  for  the  cycle  CDEFC  we  have 


nr*!t          ff 

and  for  the  entire  figure 


- 

'TT1//  'T'  / 


'T'  f 


FIG.  19. 


Any  cycle  composed  of  isothermals 
and  adiabatics  may  in  like  manner  be  divided  into  cycles,  for 
each  of  which  the  principle  holds,  and  the  summation  for  the 
whole  cycle  will  give  the  same  result  as  above. 

If  any  area  be  enclosed  by  any  curve  whatever,  as  in  Fig.  20, 
the  cycle  may  be  approximately  replaced 
by  a  complex  cycle  composed  of  isother- 
mals and  adiabatics  only,  and  for  such  a 
cycle  we  shall  have  the  same  result  as  for 
the  case  already  discussed.  As  the  curves 
are  drawn  nearer  together  the  approxi- 
mation will  be  nearer,  and  at  the  limit  by 
integration  we  have 


FIG.  20. 


rdQ_ 

J    T  ~ 


o. 


The  two  laws  of  thermodynamics  may  therefore  be  expressed 
for  closed  reversible  cycles  by  the  two  equations, 


CHAPTER   IV. 


\ 


FIG.  21. 


NON-REVERSIBLE   PROCESSES. 

SUPPOSE  that  a  body  passes  from  the  state  represented  by 
the  point  A  to  the  state  represented  by  B,  by  some  process  in 

which  the  pressure  exerted  by  the 
substance,  i.e.,  the  specific  press- 
ure, is  different  from  the  external 
pressure;  then  the  area  aABb 
represents  the  external  work  done. 
The  usual  method  for  finding 
the  change  of  intrinsic  energy  for 
a  reversible  process  is  to  draw  an 
isodynamic  line  AG  through  the 
point  A,  and  an  adiabatic  line  BG  through  the  point  B\  the 
area  bBGg  represents  the  change  of  intrinsic  energy,  and  the 
entire  area  aABGg  represents  J  times  the  heat  absorbed.  If 
the  state  of  the  substance  corresponding  to  B  is  a  state  of 
equilibrium,  then  the  process  is  equally  applicable  here.  But 
the  case  is  different  for  any  intermediate  point,  as  C ,  for  it  the 
external  work  is  represented  by  the  area  aACc,  but  the  change 
of  intrinsic  energy  is  not  represented  by  the  area  cCDd,  because 
the  body  is  not  supposed  to  be  in  equilibrium.  If,  for  example, 
a  piston  moving  in  a  cylinder  is  suddenly  and  forcibly  with- 
drawn, the  external  pressure  is  less  than  the  specific  pressure, 
and  the  substance  is  thrown  into  commotion.  Should  the 
expansion  be  arrested  at  the  point  C  and  no  heat  added  or 
abstracted,  the  body  when  it  arrives  at  equilibrium  will  have  its 
state  represented  by  the  point  E,  and  the  increase  of  intrinsic 
energy  will  be  represented  by  the  area  cEFf.  The  area  dDCEFf 
will  represent  the  energy  due  to  the  mechanical  motion  or  com- 

34 


NON-REVERSIBLE  PROCESSES.  35 

motion  of  the  substance  at  the  state  represented  by  point  C  of 
the  process. 

If  a  non-reversible  process  forms  a  cycle  so  that  the  initial 
and  final  states  are  identical,  then  the  conservation  of  energy 
will  require  that  the  equation 

fdQ  =AW 

must  hold.  On  the  other  hand,  an  investigation  of  the  value  of 
-^  will  show  that  the  integral  for  the  entire  cycle  is  negative. 

For  example,  suppose  there  is  a  reversible  engine  working  be- 
tween the  temperature  T  and  T'  and  the  entropies  0  and  0'  ; 
then  it  has  been  shown  that  the  heat  changed  into  work  at  each 
stroke  is 

(T- 


A  non-reversible  engine,  working  between  the  same  tem- 
peratures and  taking  the  same  amount  of  heat  per  stroke,  may 
have  a  less  efficiency  because  the  working  substance  has  at 
times  a  temperature  different  from  that  of  the  source  of  heat 
while  receiving  heat,  or  from  that  of  the  refrigerator  while 
yielding  heat.  In  such  case 


Q1  and  0/>  the  heat  received  and  the  heat  rejected,  being  differ- 
ent from  the  corresponding  amounts  for  the  reversible  engine, 
and  Wl  being  less  than  W.  In  like  manner,  if  (0'  —  0)  becomes 
*/0,  then,  in  general, 


and  should  the  temperature  T'  approach  zero,  then  (7^  — 
will  approach  T,  and  at  the  limit 

dQ,  < 


36  THERMODYNAMICS  OF   THE  STEAM-ENGINE. 

or,  dropping  the  subscript, 


for  a  non-reversible  cycle, 

But,  since  the  cycle  is  supposed  to  be  complete,  the  initial 
and  final  states  of  the  body  are  identical;  so  that,  integrating 
with  those  states  as  limits. 


Therefore,  for  a  non-reversible  cycle, 

=-*  .......    (43) 

in  which  N  may  have  any  value  ;  i.e.,  it  may  approach  zero. 


CHAPTER  V. 

FUNDAMENTAL  EQUATIONS. 

Application  of  the  First  Law.  —  Equations  (5)  and  (23) 
give  w 

dQ  =  A(dE  +  dW)  =  c^dt  +  ldv\  '™ 

i 
or,  replacing  dWby  pdv, 

A(dE  +  pdv)  ^  Cvdt  +  Idv  ; 


(44) 


Now  E  depends  on  the  state  of  the  body  only,  and  not  on 
the  method  of  changing  from  one  condition  to  another  ;  that 
is,  dE  is  an  exact  differential,  and  consequently 


dtdv       dvdi' 
which  may  be  written 

rdE\     \          C     tdE 


dv    "  }  t         (       ~dt 

in  which  the  partial  differential  coefficients  are  those  of  the 
equation 


Comparing  with  equation  (44),  it  appears  that 

'dE\        cv  idE 

-     =  -—        and 


37 


38  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

and  that  consequently 


dvAlt  "  dt\A 

dp 


•  •  •  (4S) 

The  combination  of  equation  (23),  which  expresses  the  first 
law  of  thermodynamics,  with  equation  (5),  is  the  application  of 
the  first  law  to  that  equation,  and  equation  (45)  is  the  relation 
between  the  latent  heat  of  expansion  and  the  specific  heat  at 
constant  volume  which  must  exist  if  that  law  be  true. 

In  a  similar  manner  the  first  law  may  be  applied  to  equa- 
tion (6),  as  follows  : 

dQ  —  A(dE  -\-pdv)  =  cpdt  +  mdp. 
Substituting  the  value  of  dv  from  the  equation 


[~ct          ldv\ 

•••  dE  =  Li  ~  A;4 


But 

4£.+  *E. 

dtdp  ~~  dpdt' 

d  I  c*          (dv  \             d  \fH          (dv  \ 
..       JL d I         - ^[ I  / 

dp  LA       F\dt  )pAt       dt\_A       *\dp  )t-^p 

fd(—\  \  ( d(~\  ' 

I  idcp\        ldv\          (     \dt  }p  ]        i  idm\          f     \dp)t 

]  -    •  )rp\dp ~  r'A\-di}-p\^t 


FUNDAMENTAL  EQUATIONS.  39 

But 


dpdt~    dtdp' 

d 


which  is  the  relation  between  the  thermal  capacity  m  and  the 
specific  heat  at  constant  pressure  developed  by  the  application 
of  the  first  law  to  equation  (6). 

Again,  the  same  law  may  be  applied  to  the  equation  (7). 

dQ  —  A(dE  -{-  pdv)  —  ndp  +  odv\ 

.....    (47) 
Since 


dpdv       dvdp* 

I  idn\          i  tdo 
'*•     Afah**.  A\# 

dn 

Application  of  the  Second  Law. — The  second  law  of 
thermodynamics  is  expressed  by  making  -=•  an  exact  differen- 
tial. Applying  this  to  equation  (5)  in  the  same  way  as  was 
done  with  the  first  law, 

dQ       cv  I 


4O  THERMODYMAMICS  OF   THE   STEAM-ENGINE. 

But 


dt  dv  dv  dt 

.    d(c*\    -  ?-(L\ 

~ 


LA  dt, 

T\dv)t  -  T*- 

dc»  I 


(49) 


the  relation  between  /  and  cv  developed  by  the  application  of 
the  second  law  to  equation  (5). 

Applying  to  equation  (6),  we  have 


-- 


d  ICL\          d_lm_ 
dp\T}t  ~  <-A~~ 


_ 
Tdpt 

ldcp\         fdm\  m 

\dp]t  " 


FUNDAMENTAL  EQUATIONS.  41 

Again,  applying  to  equation  (7), 

dQ         n 

--  =  --dp  + 


dt 


dt  tdt     n         i  do  idn 


First  and  Second  Laws  Combined.  —  The  result  of  ap- 
plying both  the  first  and  second  laws  of  thermodynamics  simul- 
taneously to  the  fundamental  equations  is  deduced  by  uniting 
the  equations  obtained  by  applying  each  separately. 

For  the  equation  (5),  in  terms  of  cv  and  /,  the  comparison 
of  equations  (45)  and  (49)  gives 


©,=  JT 

For  equation  (6),  equations  (46)  and  (50)  give 


\  -  - 

dt)-        A   T 


Also  for  equation  (7),  equations  (48)  and  (51)  give 


42  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Or,  substituting  the  values  of  n  and  o  from  equations  (17)  and 


Zeuner's  Equations.  —  In  his  Mechanische  Wdrmetheorie, 
Zeuner  employs  the  alternative  method,  so  far  as  to  deduce 
equation  (42).  Then,  instead  of  assuming  that  ,S  is  the  abso- 
lute temperature,  or  giving  such  a  definition  of  temperature,  he 
assumes  that  the  similarity  of  the  thermodynamic  equations  to 
certain  gravitation  equations  indicates  an  essential  similarity, 
and  thereby  avoids  the  second  law  of  thermodynamics.  With- 
out discussing  his  method,  there  appears  no  reason  why  it 
might  not  be  applied  to  deduce  equations  of  the  same  form  as 
those  given  here.  He,  however,  gives  equations  of  a  different 
form  which  may  readily  be  deduced  from  our  own,  and  which 
it  may  be  convenient  to  write  down  here.  Comparing  equation 
(47)  with 


it  is  evident  that 


.A  " 

forms  which  were  deduced  in  the  alternative  method  of  the 
second  law  of  thermodynamics.     These  Zeuner  writes  : 


FUNDAMENTAL  EQUATIONS.  43 

Solving  equation  (54)  for  o  and  for  n, 


o  = 


n  = 


4plv 

<«•-$). 


Substituting  the  values  successively  in  equation  (7),  we  have 
the  following  : 


But 


44  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Zeuner  deduces,  for  his  fundamental  equations, 
dQ  =  A(Xdp  +  Ydv)  ; 


dp 


which  may  readily  be  deduced  from  the  equations  above. 


CHAPTER   VI. 

PERFECT    GASES. 

THE  characteristic  equation  of  a  gas  is  the  algebraic  ex- 
pression of  the  combined  laws  of  Boyle  and  Gay  Lussac. 

;  ....   (56) 

....     (57) 


/0  and  v0  being  the  specific  pressure  and  specific  volume  at  freez- 
ing, and  OL  their  coefficient  of  dilatation  at  constant  pressure. 

Coefficient  of  Dilatation.  —  Regnault*  gives  for  the  dilata- 
tion from  freezing  to  boiling  point,  at  Paris,  the  results  : 

Hydrogen,     .........  0.3667 

Atmospheric  air,    .......  0.3665 

Nitrogen,  ..........  0.3668 

Carbonic  acid,    ...     .....  0.3688 

In  works  on  thermodynamics  it  has  been  commonly  assumed 
that  the  coefficient  of  dilatation  for  air  may  be  used  for  all 
gases,  and  at  all  temperatures  and  pressures,  and  that,  conse- 
quently, on  the  Centigrade  scale,  a  is  0.003665,  or  very  nearly 
-^¥.  Professor  Holman  f  suggests  that  as  the  pressure  ap- 
proaches zero,  the  coefficient  of  dilatation  of  all  gases 
approaches 


a  = 


2737' 


*  Memoires  de  1'Insthut  de  France,  tome  xxi. 

f  Lecture  Notes  on  Heat,  Mass.  Inst.  Technology. 

45 


46  THERMODYNAMICS  OF  THE   STEAM-ENGINE. 

which  agrees  with  thermodynamic  investigations  relating  to  the 
absolute  zero  of  temperature.     On  the  Fahrenheit  scale, 

i 

a  •=. . 

4927 

Specific  Volume. — This  quantity  is  determined  from  the 
density,  which  is  given  for  several  gases  in  the  following  table, 
at  freezing  point  and  at  atmospheric  pressure,  as  determined 
by  Regnault. 

Weight  in  grams  of  one  liter : 

Atmospheric  air, 1.293,  187 

Nitrogen, 1.256  167 

Oxygen, 1.429  802 

Hydrogen, 0.089  578 

Carbonic  acid, J-977  4*4 

The  specific  volumes  are  as  follows.  Volumes  in  cubic 
meters  of  one  kilogram,  at  Paris,  latitude  48°  50'  14" ;  elevation, 
60  meters : 

Atmospheric  air, 0.773  2834 

Nitrogen, 0.796  0724 

Oxygen,         .......  0.699  3974 

Hydrogen, 11.163  46 

Carbonic  acid, °-5°5  7IO9 

The  specific  volumes,  reduced  to  the  latitude  of  45°  at  sea 
level,  are  given  in  the  next  table. 

Volumes  in  cubic  meters  of  one  kilogram,  at  45°  of  latitude : 

Atmospheric  air, 0.773  5327  - 

Nitrogen, 0.796  3291 

Oxygen,         0.699  6231 

Hydrogen, 11.167  05 

Carbonic  acid, 0.505  8741 


PERFECT    GASES.  47 

The  reduction  for  the  change  of  the  acceleration  due  to 
gravity  is  made  by  the  equation  * 

g  —  980.6056  —  2.5028  COS  2\  —  O.OOOOO3^,        .       (58) 

in  which  g  is  the  acceleration  in  centimeters,  A.  is  the  latitude, 
and  h  is  the  elevation  above  the  sea  in  centimeters.  One  kilo- 
gram f  is  equivalent  to  2.20462125  pounds;  and  one  meter,  as 
determined  by  Professor  Rogers,  \  is  equivalent  to  39.3702 
inches,  from  which  the  specific  volume  in  English  units  may  be 
determined. 

Volumes  in  cubic  feet  of  one  pound  at  45°  of  latitude: 

Atmospheric  air, 12.3909 

Nitrogen,      .     . 12.7561 

Oxygen,  .     .'..'.'   /  .     .     .     .       11.2070 

Hydrogen,    /'.'.."   .....  178.881 
Carbonic  acid,  .,*....         8.10324 

Specific  Pressure. — The  weight  of  one  liter  of  mercury, 
determined  by  Regnault,  is  13.5959  kilograms;  consequently 
the  pressure  of  one  atmosphere,  or  760  mm.,  of  mercury  on  one 
square  meter  is 

!O333  kilograms. 

Using  the  values  given  above  for  the  kilogram  and  meter 
we  have,  for  the  English  system, 

14.6967  pounds  per  square  inch, 
2116.32  pounds  per  square  foot. 

Value  of  R. — Taking  the  value  of/, ,  v0 ,  and  or,  at  freezing 
point  and  under  the  pressure  of  760  mm.  of  mercury,  we  have 
for  air, 

*  Everett's  Units  and  Phys.  Const. 

f  Miller,  Phil.  Transactions,  cxlvi,  1856. 

|  Pro.  Am.  Acad.  of  Arts  and  Sci.,  1882-83  ;  also  additional  observations. 


48  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

French  units,  R  =  ^^  =  29.20.    .     (59) 


English  units,  R  =          '3  --  I2-39*  =  53.22.     .     (60) 

492.7 

The  value  of  R  for  other  gases  may  be  determined  in  a  like 
manner. 

Specific  Heat  at  Constant  Pressure.  —  The  specific  heat 
for  true  gases  is  very  nearly  constant,  and  may  be  considered 
to  be  so  for  thermodynamic  equations.  Regnault  gives  for 
the  mean  values  for  specific  heat  at  constant  pressure  the  fol- 
lowing results  : 

Atmospheric  air,     .......  0.2375 

Nitrogen,  .......     ...  0.2438 

Oxygen,    ..........  0.2175 

Hydrogen,     .........  3409 

Application  of  the  Two  Laws  of  Thermodynamics.— 

The  result  of  applying  the  two  laws  of  thermodynamics  to 
equation  (7)  is  given  by  equation  (55), 

*--»•£),•©.• 

Differentiating  the  characteristic  equation  (57)  for  a  gas, 
tdv\       R  idp\  __  R 


which,  substituted  in  equation  (55),  give 

(61) 


Specific  IJeat  at  Constant  Volume.  —  The  specific  heat 
at  constant  volume  has  not  been  determined  directly.     It  is 


PERFECT    GASES.  49 

evident  from  equation  (61)  that  the  assumption  of  the  charac- 
teristic equation  (57),  and  the  assumption  that  Cp  is  constant, 
make  cv  also  constant.  It  will  be  seen  subsequently  that  the 
ratio  of  the  specific  heats  may  be  determined  experimentally. 
The  ratio  is  commonly  taken  to  be 


-r  =  *  =  1405- 

cv 

Thermal  Capacities.  —  Substituting  the  values  of  the  par- 
tial differential  coefficients  as  deduced  from  equation  (57),  in 
equations  (11),  (15),  (17),  and  (18),  we  have,  for  the  values  of  the 
thermal  capacities  for  gases, 


(62) 


=  -~  (cp  -  cv)  =  -  -  —  (cp  -  cv)  ;    ,     .     .     (63) 


T 


Combining  these  four  equations  with  equation  (57)  gives 

/  —  Ap ;  .     .     .     .     .     .     .     .     .     (66) 

m=='^Av] (67) 

n=Av    ^.. (68) 

'      "6  £« 


-~ (69) 

—  c 


50  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

General  Equations. — The  values  of  the  thermal  capacities 
given  by  equations  (62),  (63),  (64),  and  (65),  substituted  in  equa- 
tions (5),  (6),  and  (7),  give 


--^;    .     .    .    .     (70) 


-dp',    ....     (71) 


T  T 

dQ  =  cv  --  dp  +  cp  —  dv. (72) 

P  v 

Just  as  the  first  law  of  thermodynamics  was  applied  to  the 
general  equations  (5),  (6),  and  (7),  by  equating  them  to  equation 
(23),  so  the  first  law  may  be  applied  to  equations  (70),  (71),  and 
(72)  in  the  same  manner.  For  example,  the  application  of  the 
first  law  to  equation  (70)  gives 


T 

dQ  =  A  (dE  +fdv)  =  cvdt  +  (cp  —  cv)-dv; 


(cp  —  c^) /  \dv 

J}  v       ^J 

d  tcn\       d  r  i  .  T 


*-*' ** 

cp—  cv  —  AR 


PERFECT    GASES.  5 1 

The  application  of  the  same  law  to  each  of  the  other  two 
equations,  (71)  and  (72),  gives  the  same  result.  The  fact  that 
the  result  is  the  same  as  that  resulting  from  the  application  of 
both  laws  of  thermodynamics  indicates  that  the  characteristic 
equation  for  gases  implies  the  second  law.  An  attempt  to  apply 
the  second  law  to  equations  (70),  (71),  and  (72)  in  the  usual 
manner  gives  in  each  case  zero  equal  to  zero,  which  reaffirms 
the  preceding  statements  in  another  form. 

Isothermal  Lines. — The  equation  to  the  isothermal  line 
for  gas  is  obtained  by  making  T  constant  in  the  general  equa- 
tion, which  gives  the  equation  representing  Boyle's  law : 

pv=PJ>.  =  const., (73) 

which  is  the  equation  to  a  rectangular  hyperbola. 

The  heat  absorbed  during  an  isothermal  change  is  obtained 
by  integrating  one  of  the  general  equations  (70),  (71),  or  (72) 
with  T  assumed  to  be  constant,  so  that  dt  becomes  zero. 

Equation  (70)  gives 


...  Q  =  (c,-cv)Tlogf%; (74) 


or?  substituting  for  the  value  of  cp  —  cv  from  equation  (68), 
In  like  manner  equation  (71)  gives 


<2  =  ('.-<>)  7*  log,        ;      .....     (76) 


,      =  Apjv.  lo&      ;       .     (77) 


52  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

which  equations  can  be  deduced  from  the  preceding  by  substi- 
tuting for  -  •  from  the  characteristic  equation. 
To  find  the  work  done,  the  equation 


/»z/, 

=   /     pdv 

t/V0 


may  be  used  after  substituting  for  /  from  the  characteristic 
equation,  whence 

W  =  f.v.  /""?=/.<*.  log  .2.    •     •     •     (78) 


z/0 


A  comparison  of  equations  (75)  and  (78)  shows  that  all  the 
heat  absorbed  is  changed  into  external  work  ;  consequently  the 
intrinsic  energy  remains  unchanged  during  the  operation. 

The  area  contained  between  the  axis  O  V, 
Fig.  22,  the  ordinate  ab,  and  the  isothermal 
line  act  extended  without  limit,  is 

W  =  pnv.  log,—  =  oo. 


FlG- 22-  This  may  also  be  seen  from  the  consid- 

eration that  if  heat  be  continually  applied,  and  all  changed 
into  work,  there  will  be  a  limitless  supply  of  work. 

Isoenergic  or  Isodynamic  Lines. — In  the  discussion 
of  isothermal  lines  it  appears  that  all  the  heat  received  is 
changed  into  work ;  consequently  the  intrinsic  energy  remains 
constant  during  an  isothermal  change.  From  which  it  is  appar- 
ent that  the  isoenergic  line  is  coincident  with  the  isothermal 
line. 

From  the  importance  of  the  subject,  an  independent  proof 
will  be  given  that  E  is  a  function  of  /  only. 


PERFECT    GASES.  53 

Comparing  with  equation  (71),  it  is  apparent  that 

• 


Again, 


Comparing  with  equation  (72),  it  is  apparent  that 

.  +>(&]-(*-*  )f 


The  importance  of  the  proposition  that  E  is  a  function  of  / 
only,  will  be  apparent  in  connection  with  the  comparison  of  the 
scale  of  the  air  thermometer  with  the  thermodynamic  scale. 

Adiabatic  Lines.  —  During  an  adiabatic  change,  for  exam- 
ple, the  expansion  of  a  gas  in  a  non-conducting  cylinder,  heat 
is  not  communicated  to,  nor  abstracted  from,  the  gas  ;  conse- 
quently dQ  in  equations  (70),  (71),  and  (72)  becomes  zero. 

From  equation  (72), 


Cp  dv  _        dp 

Tv  v  ~       p  ' 


54  THERMODYNAMICS  OF  THE   STEAM-ENGINE. 

The  ratio  —  of  the  specific  heats  may  be  represented  by  /r, 
and  the  above  equation  may  be  written 


.•.  v*p  —  v^p0  —  const  ......     (80) 

From  equations  (70)  and  (71), 

z,"-'  T  =  V~x  T*  =  const,  .    .    .    .  '(81) 


TP*    =  TK~  *  =  const  ;'    •    •    •    (82> 

or  these  last  two  equations  may  be  deduced  from  equation  (80) 
by  substituting  for  p  or  for  v  from  the  characteristic  equation. 
To  find  the  external  work,  the  equation 

W=fpdv 
may  be  used  after  substituting  for/  from  equation  (79)  or  (80). 

fv*  Cv*dv  p.v.*    (     i  i     \ 

W  =   I     pdv  =  v*p,  I      —  =  —  ^-^-    ---    ; 

t/ZV  V  ^  t/Z/j  ^  K   _     l     \v     K.  -   I  K   -  I/ 


In  Fig.  23  the  area  between  the  axis  OV, 
the  ordinate  ba,  and  the  adiabatic  line  aa  ex- 
tended  without  limit  becomes 


FIG.  23. 

and  not  infinity,  as  is  the  case  with  the  isothermal  line. 


PERFECT    GASES.  55 

Intrinsic  Energy.  —  Since  the  external  work  is  done  at  the 
expense  of  the  intrinsic  energy,  the  work  obtainable  by  an  in- 
finite expansion  cannot  be  greater  than  the  intrinsic  energy. 
If  it  be  admitted  that  when  the  volume  becomes  infinity  and 
the  pressure  and  temperature  become  zero,  the  intrinsic  energy 
becomes  zero,  then  we  shall  have 


which  gives  a  method  of  calculating  the  intrinsic  energy. 

Though  such  a  method  of  calculating  the  intrinsic  energy 
is  subject  to  an  error,  from  the  fact  that  at  zero  temperature 
and  pressure  the  intrinsic  energy  is  not  zero,  the  error  is  con- 
stant for  all  values  of  intrinsic  energy,  and  disappears  when 
differences  are  taken. 

Entropy.  —  From  equation  (71)  we  have 

dQ        dt  dp 

—  =  cj—  +  (cv  —  c/)—, 

which,  for  a  reversible  cycle,  is  equal  to  the  differential  of  the 
entropy.    Consequently  we  have,  on  integrating  between  limits, 


0-  00  =  ^log,^  +  (^-^)log,-.  .     .     .     (85) 

•*•  o  /o 

This  gives  a  method  of  calculating  the  increase  of  entropy 
above  that  at  a  certain  state  ;  for  example,  above  that  at  freez- 
ing-point and  under  normal  atmospheric  pressure. 

Similar  expressions  maybe  deduced  from  equations  (70)  and 

(72). 

Carnot's  Cycle.  —  It  has  already  been  shown  that  the  char- 
acteristic equation  for  a  gas  implies  the  second  law  of  ther- 
modynamics, but  it  can  be  shown  in  another  and  more  direct 
way  by  aid  of  Carnot's  cycle.  The  demonstration  is  frequently 
given  in  elementary  works,  and  may  be  useful  as  an  exercise. 


56 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


The  equation  to  the  isothermal  line  for  a  gas  was  deduced 
from  the  characteristic  equation  by  making 
T  a  constant,  and  the  equation  to  the  adia- 
batic  line  was  deduced  from  equation  (72)  by 
making  dQ  equal  to  zero  ;  in  all  of  which  no 
direct  reference  was  made  to  the  second  law 
of  thermodynamics,  or  the  efficiency  of  a 
reversible  engine.  Let  us  now  consider  the 
cycle  of  Carnot's  engine  for  a  perfect  gas. 

We  shall  have,  as  in  the  general  case,  that  the  area  of  ABCDA 

(Fig.  24)  represents  the  work  done  ;  that  is, 


FIG. 


24. 


W= 


Wtc-  Wcd-  W4a.     ...    (86) 


Since  AB  and  DC  are  isothermal  lines, 


(87) 


(88) 


and  since  BC  and  DA  are  adiabatic  lines 


The  last  two  quantities  of  work  are  equal,  for  we  have 


PERFECT    GASES.  57 

because  the  points  a  and  b  are  on  the  same  isothermal  line ; 
and  since  a  and  d  are  on  one  adiabatic  line,  and  b  and  c  are  on 
another,  we  have 


-  T ,  , 

»*•  1  -  * 

Tl  being  the  absolute  temperature  of  the  isothermal  line  AB, 
and  T;  of  Z>C\ 

The  last  two  equations  give  also 

va      vb  va  _  Vd 

vd  ~  vc  '  vb  ~~  vc  ' 

and  the  characteristic  equation  gives 

PaVa  =  RT1}  pdVd  =  RT^  J 

whence  equations  (87)  and  (88)  reduce  to 


e 


and  these  values  inserted  in  equation  (86)  give 


To  calculate  the  heat  received  by  the  working  substance  in 
passing  along  the  isothermal  from  A  to  B,  we  may  employ 
equation  (65)  with  the  condition  that  T  shall  be  constant,  and 
dt  shall  be  zero.  Integration  between  limits  gives 


58  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

which,  by  aid  of  equation  (68),  may  be  reduced  to 

a  =  ^2",log,£. 

Now  the  efficiency  of  any  engine  is 


from  which  the  efficiency  of  an  air-engine,  working  on  Carnot's 
cycle,  is 


Comparison  of  the  Air  Thermometer  with  the  Absolute 
Scale. — In  connection  with  the  isodynamic  line  it  was  shown 
that  the  intrinsic  energy  is  a  function  of  the  temperature  only. 
This  conclusion  is  deduced  from  the  characteristic  equation  on 
the  assumption  that  the  scale  of  the  air  thermometer  coincides 
with  the  thermodynamic  scale,  and  affords  a  delicate  method 
of  testing  the  truth  of  the  characteristic  equation,  and  of  com- 
paring the  two  scales. 

The  most  complete  experiments  for  this  purpose  were  made 
by  Joule  and  Sir  William  Thomson,  who  forced  air  slowly 
through  a  porous  plug  in  a  tube  in  such  a  manner  that  no  heat 
was  transmitted  to  or  from  the  air  during  the  process.  Also  the 
velocity  both  before  and  beyond  the  plug  were  so  small  that 
the  work  due  to  the  change  of  velocity  could  be  disregarded. 
All  the  work  that  would  be  developed  in  free  expansion  from 
the  higher  to  the  lower  pressure  was  used  in  overcoming  the 
resistance  of  friction  in  the  plug  and  so  converted  into  heat, 


PERFECT    GASES. 


59 


and  as  none  of  this  heat  escaped  it  was  retained  by  the  air 
itself,  the  plug  remaining  at  a  constant  temperature.  It  there- 
fore appears  that  the  intrinsic  energy  remained  the  same,  and 
that  a  change  of  temperature  indicated  a  deviation  from  the 
assumptions  of  the  theory  of  perfect  gases.  The  change, 
though  slight,  was  measurable,  and  has  been  used  to  establish 
the  comparison  between  the  two  thermal  scales  under  dis- 
cussion. 

In  the  discussion  of  results  given  by  Joule  and  Thomson  * 
in  1854  they  give  for  the  absolute  temperature  of  freezing- 
point,  273°. 7  C.  As  the  result  of  later  f  experiments  they  state 
that  the  cooling  for  a  difference  of  pressure  of  100  inches  of 
mercury  is  represented,  on  the  Centigrade  scale,  by 


0°.92 


The  following  table  shows  the  agreement  between  this  state- 
ment and  the  results  of  experiment : 

FLOW   OF   AIR    THROUGH    POROUS    PLUG. 


COOLING  EFFECT  — 

By  Experiment. 

By  Calculation. 

o° 

0.92 

0.92 

7-1 

0.88 

0.87 

39-5 

o-75 

0.70 

92.8 

0.51 

0.51 

From  the  work  of  these  experiments  Rowland  \  deduced  the 
following  comparison  of  the  air  thermometer  with  constant 
volume,  with  the  absolute  thermodynamic  scale  of  temperature. 


*  Philosophical  Transactions,  vol.  144,  p.  349. 

f  Ibid.,  vol.  152,  p.  579. 

\  Proceedings  of  the  American  Academy,  vol.  xv.  (N.  S.  viii.)  p.  75;  1879. 


6o 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


REDUCTION   OF  THE  AIR  THERMOMETER  TO   THE 
ABSOLUTE  SCALE. 

(Centigrade.) 


TEMPERATURE  ABOVE  FREEZING. 

Correction  to  Air 
Thermometer. 

Air  Thermometer. 

Absolute  Scale. 

O° 

' 

o 

10 

9.9972 

—  0.0028 

20 

19.9952 

—  0.0048 

30 

29.9939 

—  0.0061 

40 

39-9933 

—  0.0067 

50 

49.9932 

—  0.0068 

60 

59-9937 

—  0.0063 

70 

69.9946 

—  0.0054 

80 

79-9956 

—  0.0044 

90 

89.9978 

—  0.0022 

IOO 

100.000 

O. 

200 

200.037 

+  0.037 

300 

300.092 

+0.092 

^       4OO 

400.157 

+0.157 

500 

500.228 

+  O.228 

C     AB 


FIG.  25. 


Velocity  of  Sound. — Sound  is  transmitted  through  the  air 
in  spherical  waves,  but  at  a  distance  from  the  source  of  sound 
the  waves  are  sensibly  plane  waves,  and 
~  the  progress  of  the  wave  is  the  same  as 
—  that  of  a  plane  wave  in  a  straight  tube  of 
uniform  section.  Let  Fig.  25  represent  a 
tube  one  square  meter  in  section,  in  which  a  wave  moves  with 
a  linear  velocity  UQ  meters  per  second ;  that  is,  a  point  at  a  given 
phase  of  the  wave,  for  example,  C  at  the  greatest  condensa- 
tion, moves  at  that  velocity. 

Since  the  wave  moves  with  the  velocity  u0 ,  the  volume  of 
air  disturbed  in  a  unit  of  time  is  UQ  cubic  meters.  If  the 
specific  volume  in  the  undisturbed  state  is  z>0 ,  then  the  weight 
of  air  disturbed  in  a  second  is 


w  =  mg  =  —  ; 


m  being  the  mass  of  air  which  has  the  weight  w. 


PERFECT    GASES.  6  1 

Imagine  two  planes  A  and  B  at  a  small  distance  apart,  which 
also  move  with  the  velocity  u0  ,  so  that  they  remain  at  the  same 
phase  of  the  w*ave.  Let  the  absolute  velocities  of  the  air  at 
these  planes  be  ul  and  uz  ;  then  the  velocities  of  the  air  through 
the  planes,  that  is,  the  velocities  relatively  to  the  planes,  is,  for 
A,  u0  —  ul  ,  and  for  B,  u0  —  u^.  With  vl  and  v^  for  the  specific 
volumes  at  these  planes,  the  weights  that  pass  through  the 
planes  A  and  B  per  second  are 


and 


Since  the  phase  of  that  portion  of  the  wave  between  A  and 
B  is  constant,  the  weight  of  the  air  between  them  is  also  con- 
stant, and  as  much  air  enters  per  second  as  leaves  during  that 
time.  Again  :  as,  on  the  whole,  the  air  is  not  transmitted,  but 
only  compressed  and  rarefied,  the  whole  air  disturbed  per 
second  must  pass  through  the  space  between  the  planes. 
Therefore, 


=       = 

V,  V, 


Now,  as  the  mass  m  enters  the  space  between  the  planes 
with  the  absolute  velocity  u1  ,  and  an  equal  mass  leaves  with 
the  velocity  u^  ,  consequently  there  is  a  change  of  momentum 

m  (u,  —  u^  ; 

and  since  this  cannot  come  from  the  mutual  action  of  the  par- 
ticles, it  must  come  from  the  difference  of  pressures  at  A  and 
B\  thus, 

A  -  A  =  m  («i  -  O  = 


62  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

As  the  planes  A  and  B  approach  each  other,  pl  and  /,  ,  vl 
and  v^  approach  in  value,  and  at  the  limit 

dp  =  —  m*gdv, 

dp  i  u: 

-j  -  =  —  m-g  =  ---  1  ; 
dv  g  v* 

the  last  reduction  being  obtained  by  substituting  for  the  value 
of  m  from  the  preceding  work.     Solving  for  UQ  , 


The  vibrations  are  so  rapid  that  the  changes  of  state  may 
be  assumed  to  be  adiabatic  ;  consequently  equation  (72)  gives 


__  =__ 

dv  cv  '  v  v  ' 

The  planes  A  and  B  may  be  taken  at  any  phase  of  the 
wave  ;  for  example,  at  the  phase  where  the  pressure  and  volume 
are  normal,  in  which  case 


_ 

1      -   —~  K  • 

dv  v0 

Substituting  in  the  equation  for  u0  ,  we  have 

,  ........     (90) 


The  equation  is  commonly  given  in  terms  of  the  density,  y, 
as  follows  : 


(90 


PERFECT    GASES.  63 

Ratio  of  the  Specific  Heats. — The  velocity  of  sound  from 
direct  experiment  was  found  by  Moll  and  Van  Beek  to  be 
332.26  meters  per  second  ;  by  Regnault  to  be  330.70  meters  per 
second.  Kayser  found  from  Kundt's  dust  figures  the  wave 
length  corresponding  to  a  certain  tone,  and  therefrom  deduced 
the  velocity  of  sound,  and  gives  for  the  velocity  332.50  meters 
per  second.  The  true  value  must  be  nearly  332  meters  per 
second.  Solving  equation  (9^  for  /c,  and  intersecting  the 
known  values  of/0z/0  and  g  for  Paris, 


K=  "•'  =        332 

gv,p,   9.8092  X  0.77328  X  10333  ' 


Direct  experiments  to  determine  K  may  be  made  as  follows  : 
Suppose  that  a  vessel  is  filled  with  air  at  a  pressure  pl,  while 
the  pressure  of  the  atmosphere  is/0  .  Let  a  communication  be 
opened  with  the  atmosphere  sufficient  to  suddenly  equalize  the 
pressure  ;  then  let  it  be  closed,  and  let  the  pressure  p^  be  ob- 
served after  the  air  has  again  attained  the  temperature  of  the 
atmosphere.  If  the  first  operation  is  sufficiently  rapid  it  may 
be  assumed  to  be  adiabatic,  and  we  may  use  equation  (79),  from 
which 


!og  %  —  log  ^i 


,    . 


The  second  operation  is  at  constant  volume  ;  consequently 
the  specific  volume  is  the  same  at  the  final  state  as  after  the 
adiabatic  expansion  of  the  first  operation.  But  the  initial  and 
final  temperatures  are  the  same  ;  consequently 

*i  A  =  v0  A  ; 

.  •  .  log  v.  -  log  v,  =  log/,  —  log  A, 


64  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

which,  substituted  in  equation  (92),  gives 

_  log  A -log /0 
log  ft  -log// 

The  same  experiment  may  be  made  by  rarefying  the  air  in 
the  vessel,  in  which  case  the  sign  of  the  second  term  changes. 

Rongten  *  employed  this  method,  using  a  vessel  containing 
70  liters,  and  measuring  the  pressure  with  a  gauge  on  the  same 
principle  as  the  aneroid  barometer.  Instead  of  assuming  the 
pressure /0  at  the  instant  of  closing  the  stop-cock  to  be  that  of 
the  atmosphere,  he  measured  it  with  the  same  instrument.  A 
mean  of  ten  experiments  on  air  gave 

K=   1.4053. 

Again,  from  equation  (68)  we  have 

=f>=  ,;v 


cv~          AR' 
i  ~~ 

CP 

i 


K  = 


_         10333  X  0./7353 
426.9  X  273.7  X  0.2375 

K  =   1.4046. 

The  value  of  K  already  given  on  page  49  will  be  used 
throughout  our  work,  i.e., 

K  =  1.405. 

Solution  of  Problems.  —  The  greater  part  of  engineering 
problems  involving  gases  may  be  solved  by  the  aid  of  the  char- 
acteristic equation 


Poggendorff's  Annalen,  vol.  cxlviii.  p.  580. 


PERFECT    GASES.  65 

or  the  equivalent  equation, 


In  the  first  of  these  two  equations  the  specific  pressure  and 
volume  to  be  used  for  English  measures  are  pounds  per  square 
foot,  and  the  volume,  in  cubic  feet,  of  one  pound. 

For  example,  let  it  be  required  to  find  the  volume  of  3  pounds 
of  air  at  60  pounds  gauge  pressure  and  at  100°  F.  Assuming 
a  barometric  pressure  of  14.7  pounds  per  square  inch, 

iv 

53.22(460.7+  100) 
*=     047  +  *»).  «  J  =  ^3  cub.c  feet 


is  the  volume  of  i  pound  of  air  under  the  given  conditions,  and 
3  pounds  will  have  a  volume 

V 

3  x  2.773  =  8.319  cubic  feet. 

The  second  equation  has  the  advantage  that  any  units  may 
be  used,  and  that  it  need  not  be  restricted  to  one  unit  of  weight. 

For  example,  let  the  volume  of  a  given  weight  of  gas,  at 
100°  C.  and  at  atmospheric  pressure,  be  2  cubic  yards;  required 
the  volume  at  200°  C.  and  at  10  atmospheres.  Here 


i  X  2 


473-7        373-7 


=  °'2535 


66  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


EXAMPLES. 

1.  Find  the  weight  of  4  cubic  meters  of  hydrogen  at  30°  C. 
and  under  the  pressure  of  800  mm.  of  mercury. 

2.  Find  the  volume  of  3  pounds  of  nitrogen  at  a  pressure  of 
^45  pounds  to  the  square  inch  by  the  gauge,  and  at  80°  F.      /  G-  3  ^ 

3.  Find  the  temperature  at  which  one  kilogram  of  air  will 
occupy  one  cubic  meter  when  at  a  pressure  of  20,000  kilograms 
per  square  meter.  //  / 

4.  Find  the  pressure  at  which  2  pounds  of  carbonic  acid  at 
freezing-point  of  water  will  occupy  3  cubic  feet.  1 

5.  A  gas-receiver  having  the  volume  of  3  cubic  feet    con-.fl1" 
tains  half  a  pound  of  oxygen  at  70°  F.     What  is  the  pressure  ?  ' 

6.  A  spherical  balloon  20  feet  in  diameter  is  to  be  inflated 
with   hydrogen  at  60°  F.  when  the  barometer  stands  at  30.2 
inches,  so  that  gas  may  not  be  lost  on  account  of  expansion 
when  it  has  risen  till  the  barometer  stands  at  19.6  inches,  and 
the  temperature  falls  to  40°  F.     How  many  pounds  and  how 
many  cubic  feet  are  to  be  run  in  ? 

7.  A  gas-receiver  holds  14  ounces  of  nitrogen  at  20°  C.  and 
under  a  pressure  of  29.6  inches  of  mercury.     How  many  will  it 
hold  at  3^°  F.  and  at  the  normal  pressure  of  760  mm.  ? 

8.  Two  cubic  feet  'of  air  expand  at  50°  F.,  from  a  pressure 
of  80  pounds  to  a  pressure  of  60  pounds,  by  the  gauge.    What 
is  the  external  work  ?  

9.  What  would  have  been  the   external  work  had  the  air 
expanded  adiabatically? 

10.  Find  the  external  work  of  2  pounds  of  air  which  ex- 
'nands   adiabatically    until    it  doubles  its  volume;    the    initial 

pressure  being   100  pounds  absolute,  and  the  initial  tempera- 
ture 100°  F. 

11.  Find  the  external  work  of  one  kilogram  of  hydrogen 
which,  starting  with  the  pressure  of  four  atmospheres  and  with 
the  temperature  of  500°  C.,  expands  till  the  temperature  be- 
comes 30°  C. 

12.  Find  the  intrinsic  energy  of  one  pound  of  the  several 


PERFECT    GASES,  6? 

gases  for  which  the  proper  data  are  given,  under  the  standard 
pressure  of  one  atmosphere  and  at  freezing-point  of  water. 

13.  A  pound  of  air  has  the  volume  6  cubic  feet  under  the 
pressure  of  30  pounds  absolute  to  the  square  inch.     Find  the 
intrinsic  energy. 

14.  In  example  13,  find  the  increase  of  entropy  above  that 
at  atmospheric  pressure  and  at  freezing-point. 

15.  A  kilogram  of  oxygen  at  the  pressure  of  6  atmospheres 
and  at  100°  C.  expands  isothermally  till  it  doubles  its  volume. 
Find  the  change  of  entropy. 

16.  Suppose  a  hot-air  engine,  in  which  the  maximum  pres- 
sure is  100  pounds  absolute,  and  the  maximum  temperature  is 
600°  F.,  to  work  on  a  Carnot's  cycle.    Let  the  initial  volume  be  2 
cubic  feet,  let  the  volume  after  isothermal  expansion  be  5  cubic 
feet,  and  the  volume  after  adiabatic  expansion  be  8  cubic  feet. 
Find  the  external  work  of  one  cycle ;  also  the  horse-power  if 
the   engine   is   double-acting   and   makes   30  revolutions    per 
minute. 


CHAPTER   VII. 

SATURATED    VAPOR. 

OUR  knowledge  of  the  properties  of  saturated  vapors  is  de- 
rived mainly  from  the  experiments  made  by  Regnault.*  In 
almost  all  cases  the  results  of  the  experiments  are  stated  in  form 
of  empirical  equations  designed  to  be  used  for  calculating 
tables ;  and  since  such  tables  are  of  great  value  and  importance 
in  steam-engineering,  it  appears  advisable  to  give  at  some 
length  the  data  on  which  those  equations  are  based,  so  as  to 
show  the  limits  of  their  application  and  their  degree  of  accu- 
racy. In  some  cases  the  constants  of  the  equations  have  been 
recalculated ;  notably  in  the  case  of  the  pressure  of  saturated 
steam,  which  appeared  to  be  necessary  on  account  of  the  diver- 
sity of  the  values  given  by  different  authors  for  the  constants 
in  the  empirical  equations  used  for  calculating  tables,  and  on 
account  of  the  discrepancy  between  the  steam  tables  in  com- 
mon use,  especially  on  the  English  system  of  units. 

Pressure  of  Saturated  Vapor. — Regnault's  experiments 
on  the  temperature  of  saturated  vapor  consisted  essentially  in 
taking  the  temperature  of  the  boiling-point  of  the  vapor  under 
varying  pressures  of  the  atmosphere,  the  apparatus  being  so 
arranged  that  the  pressure  could  be  varied  from  a  small  frac- 
tion of  an  atmosphere  to  more  than  twenty  atmospheres.  The 
temperature  was  taken  with  mercurial  thermometers,  and  the 
pressures  were  measured  by  a  mercury  column,  and,  after  the 
necessary  corrections  were  applied  and  temperatures  were  re- 
duced to  the  air  thermometer,  Regnault  selected  the  results  he 
deemed  most  trustworthy,  and  plotted  a  series  of  points,  and 

*  Memoires  de  1'Institut  de  France,  etc.,  tome  xxvi. 

68 


SATURATED    VAPOR. 


then  drew  a  smooth  curve  to  represent  the  whole  series  of  ex- 
periments. 

He  then  selected  points  on  the  experimental  curve  at  regu-    ' 
lar  intervals,  and  with  these  points  as  data  he  calculated   the 
constants  of  empirical  formulae  for  use  in  calculating  the  tabular 
values.     The  formula  selected  was  of  the  form 

log/  =  *+£««  +  */?«,     .....     (94) 

in  which/  is  the  pressure,  and  n  is  the  temperature  minus  the 
constant  temperature  /„  of  the  lowest  limit  of  the  range  of  tem- 
perature to  which  the  formula  applies  ;  i.e., 

»=/—/.. 

Let  the  points  through  which  the  curve  represented  by  the 
equation  is  to  pass  be  (/„,  /„),  (A,  /,),  (A,  0»  (A>  '•)»  and  (A»  *«)» 
so  chosen  that 

*i  -*.  =  ',-  t,  =/,  -  /,  =  t,  -  /,. 


Substituting  the  five  known  values  of/  and  £  in  equation  (94), 


logA  =  «  + 
logA  =  «  + 

10g/3    =    *   + 

log/4  =  tf  + 


-^  + 


+  cj3 


4(fl  '/o) 


-    .    •    (95) 


Now  subtract  each  equation,  member  for  member,  from  the 
one  below  it,  and  for  convenience  let 

log  A  —  log  A  =  Jo>    etc.,    a'l-'*  =  m,   /3fl~^  =  n. 
.'.  y0  =  (m  — 

>.  ...  (96) 


70  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Solving  the  several  equations  for  c  and  equating  the  values, 
y0  —  ( m  —  I )  b y,  —  (m*  —  m)  b 


_y^  (nf^nf^  _  y^-W-  m3}  b 
n*  _  „•  „•  _  n* 

Again,  solving  for  b  and  equating  the  values  and  reducing 


n  —  m        (n  —  m)  m      (n  —  m)  m*  * 


.:  mny.  —  my,  =  ny,  — 
mny,  —  my^  =  ny^  — 


.    B   (Q8) 


y\ 

.....     (99) 


**='•  ~-"^'  =  N. 


Equations  (98)  and  (99)  enable  us  to  calculate  numerically 
the  values  of  M  and  N  from  the  five  given  values  of  log  /. 
Then  solving  for  m  and  n, 

M       (M*       A7V 

m  = N]  ; 

2^4  / 

M 


Solving  one  of  the  equations  (97)  for  b, 


n(m—i)  —  (m*  —  m)      (m  —\](n—m) 


SATURATED    VAPOR.  ,       71 

Again,  solving  the  first  equation  of  (96)  for  c, 


"*      __     _     SI  "VO  /mcA 

n.-  i          -(n-i}(n-my 
From  the  first  equation  of  (95), 

Finally,     a  =  mfi-<°; (104) 


(105) 


For  temperatures  below  freezing-point  Regnault  used  the 
equation 

p  —  a-\-ban, (Jo6) 

which  is  an  equation  to  a  curve  passing  through  three  points 
at  equidistant  temperatures,  and  of  which  the  solution  is  very 
simple. 

Regnault's  Data  and  Equations  for  Steam. — For  equa- 
tion (106)  the  data  are  : 

t0  =  —  32°  C.        /0  =  0.32  mm.  of  mercury. 
t,  =  -  1 6°  C.        /,  =  1.29     " 
*„  =        0°  C.        /,  =  4.60    " 

From  which  Regnault  calculated  the  following  equation,  by  aid 
of  seven-place  logarithms : 

A.  For  steam  from  —  32°  to  o°  C., 

p  —  a  ~\-  ban  ; 

a  =  —  0.08038  ; 
log  b  =  9.6024724  —  10  ; 
log  a  =  0.033398  ; 

n  =  32°  -  /. 


72  THERMODYNAMICS  OF   THE   STEAM-ENGINE, 

Regnault  gives  three  equations  of  the  form  given  by  equa- 
tion (97),  of  which  the  following  are  the  data  : 

B.        £0  =  o°  C.  A  =         4.60  mm.  of  mercury. 

/l=  25°  C.  A  =  23.55    « 

t,=  50°  C.  /,=  91.98 

*s  =  75°  C.  /.=  288.50 


« 
" 


A  = 


"  " 


C.   t.  =  100°  C.  A  =  760 

^=130°  C.  /1=  2030 

tt=  1 60°  C.  A=  4651.6   "      " 

/3  =  190°  C.  A  =  9426    "      " 

C.  A  = 


D.     /0=:-200C.  /0=  0.91  " 

/1  =  +4o°C.  A=  54.9i  " 

/,  =  100°  C.  A  =  760  '  "      " 

/,=  160°  C.  /.=  4651.6  " 
C. 


And  from  these  data  he  calculated,  by  aid  of  seven-place 
logarithms,  the  following  equations,  which  are  correct  at  Paris  : 

B.  For  steam  from  o°  to  100°  C., 

log  p  =  a  —  botn  -|-  cftn  ; 

a  —  4.7384380; 
log  b  =  0.6116485  ; 
log  c  =  8.1340339  —  10  ; 
log  a  =  9.9967249  -  10  ; 
log  /3  =  0.006865036  ; 

n  =  t. 


SATURATED    VAPOR.  73 

C.  For  steam  from  100°  to  220°  C, 

log  /  =  a  —  ba.n  -\-  eft"  ; 

a  =  54583895 ; 

log  b  =  0.4121470; 
log  c  =  7.7448901  —  10; 
log  a  =  9.997412127  —  10; 
log  ft  =  0.007590697  ; 
n  =  t  —  100. 

D.  For  steam  from  —  20°  to  220°  C., 

log  p  =  a  —  ban  —  cftn  ; 

a  =  6.2640348  ; 
log  £  =  0.1397743; 
log  c  =  0.69243  5 1  ; 
log  a  =  9.994049292  ; 
log  ft  =  9.998343862  ; 

n  =  t  +  20. 

The  temperatures  and  pressures  of  saturated  steam  in  the 
tables  given  by  Regnault  were  calculated  by  equations  A  and 
B  for  their  respective  ranges,  but  equation  D  was  used  instead 
of  C  for  temperatures  above  100°  C. 

Wishing  to  attain  greater  accuracy  for  meteorological  work, 
Moritz  recalculated  equation  B,  using  ten-place  logarithms 
and  obtained  constants  that  differed  but  little  from  those  which 
will  be  given  later.  Some  of  the  more  recent  tables  in  the 
French  system  were  calculated  by  aid  of  his  equation. 

Equations  for  the  Pressure  of  Steam  at  Paris. — In 
view  of  the  preceding  statements  it  appeared  desirable  to  re- 
calculate the  constants  for  equations  B  and  C  with  such  a  degree 
of  accuracy  as  to  exclude  any  doubt  as  to  the  reliability  of  the 
results.  Accordingly  the  logarithms  of  the  five  values  of  /  for 
each  equation  were  taken  from  Vega's  ten-place  table,  and  then 
the  remainder  of  the  calculations  were  carried  on  with  natural 
numbers,  checking  by  independent  methods,  with  the  follow- 
ing results : 


74 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


B.  For  steam  from  o°  to  100°  C, 

log  p  —  a  —  ban  +  eft* ; 

0  =  4.7393622142; 
log  £  =  0.6117400190; 
log  c  —  8.1320378383  —  10  ; 
log  a  —  9.996725532820  -  10  ; 
log  ft  =  0.006864675924  ; 

n  —  t. 

C.  For  steam  from  100°  to  220  C., 

log  /  =  a  —  ban  -f-  eft*  ; 

a=  5.4574301234; 
log  £  =  0.4119787931  ; 
log  c  =  7.7417476470  —  10 ; 
log  a  =  9.99741 106346  —  10  ; 
log  ft  —  0.0076424891 13  ; 

n  —  t  —  100. 

To  show  the  degree  of  accuracy  attained,  the  following 
tables  are  given : 

EQUATION   B. 


t. 

A 

log/  from  table  of 
logarithms. 

log/  calculated  by 
equation. 

o 

46O 

o  6627^78^17 

25 
50 

75 

100 

23.55 
91.98 
288.50 
760 

1.3719909115 
1.9636934052 
2.4601458175 
2.8808135923 

1.37199097 
1.96369346 
2.46014587 
2.88081365 

EQUATION   C. 


t. 

A 

lojp  p  from  table  of 
logarithms. 

log  /calculated  by 
equation. 

IOO 

760 

2.88o8l3^Q23 

130 

160 
190 

220 

2O3O 
4651.6 
9426 
17390 

3   3074960379 
3.6676023618 

3.9743274354 
4.2402995820, 

3.307496036 
3.667602359 
3.974327428 
4.240299575 

SATURATED    VAPOR.  75 

The  results  from  equation  Care  quite  satisfactory,  for  the 
errors  come  in  the  ninth  place  of  decimals,  and  one  place  of 
decimals  is  unavoidably  lost  in  the  application  of  the  formula. 
Equation  B  was  calculated  after  equation  C,  and  the  numerical 
work  was  not  carried  to  so  large  a  number  of  decimal  places. 
For  the  calculation  of  tables,  the  constants  are  carried  to  seven 
places  of  significant  figures  only  ;  this  gives  six  places  in  the 
result,  of  which  five  are  recorded  in  the  table. 

Pressure  of  Steam  at  Latitude  45°,  —  French  System.  — 
It  is  customary  to  reduce  all  measurements  to  the  latitude  of  45°, 
and  to  sea  level.  The  standard  thermometer  should  then  have 
its  boiling  and  freezing  points  determined  under,  or  reduced  to, 
such  conditions.  The  value  of  g,  the  acceleration  due  to 
gravity  given  by  equation  (58),  is  9.809218  meters  at  Paris, 
latitude  48°  50'  14",  and  at  an  elevation  of  60  meters.  At  45° 
and  at  sea  level,  g  =  9.806056  ;  consequently  760  mm.  of  mer- 
cury at  45°  latitude  give  a  pressure  equal  to  that  of 

980.6056 
760  X  G^l8  =  759-755  mm. 

at  Paris,  and  by  equation  B  this  corresponds  to  a  temperature 
of  99°.99i  C.  In  other  words,  the  thermometer  which  is  stand- 
ard at  45°  has  each  degree  0.99991  of  the  length  of  the  degree 
of  a  thermometer  standard  at  Paris. 

Again,  we  have  that  the  height  of  a  column  of  mercury  at 

45°  latitude  is    8o6oc;6  times  the  height  of  a  column  which  will 

give  the  same  pressure  at  Paris.  Consequently,  to  reduce  equa- 
tion B  to  45°  latitude,  we  have 


log/  =  a  +  log  '  -  <fo  0-99991  /  +  ,;/?  0.9999". 

980.6056 
and  for  equation  C, 

=  a  -f-  log  i|pf£L  _  fa  (0.99991  jf-  too)  J_  £^(0.99991  /-too) 

980.6056 

980.9218 
=  a  +  log  —  -  —  ba~  °-°°9  a  0.99991  (t  -  100) 

-f-  Cft  ~  °-°°9  ft  0.99991  (t  -  100)  ^ 


76  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

The  resulting  equations  are  : 

B.  For  steam  from  o°  to  100°  C.  at  45°  latitude, 

log  p  =  a1  —  6a*  +  c/3*; 

*i  =  47395022  ; 
log  b  —  0.6  1  17400190  ; 
log  c  —  8.1320378383  —  10  ; 
logor,  =  9.996725827522  —  10  ; 
log  ft  ^=  0.006864058103  ; 

n  =  t. 

C.  For  steam  from  100°  to  220°  C.  at  45°  latitude, 


*i  =  5-4575701  ; 
log  ^  =  0.4  1  2002093  5; 

log  cl  =  7.7416788646  —  10  ; 
log  al=  9.99741  1296464  -  10  ; 
logftt  =  0.007641801289; 
n  =  t  —  100. 

Pressure  of  Steam  at  Latitude  45°,—  English  System.— 

To  reduce  the  equations  for  the  pressure  of  steam,  so  that 
they  will  give  the  pressures  in  pounds  on  the  square  inch  for 
degrees  Fahrenheit,  there  are  required  the  comparison  of 
measures  of  length  and  of  weight,  the  comparison  of  the  scales 
of  the  thermometers,  and  the  specific  gravity  of  mercury. 

Professor  Rogers*  gives  for  the  length  of  the  meter,  39.3702 
inches.  This  differs  from  the  value  given  by  Captain  Clarke  f 
by  an  amount  that  does  not  affect  the  values  in  the  tables  ;  his 
value  being  39.370432  inches. 

Professor  Miller  J  gives  for  the  weight  of  one  kilogram, 
2.20462125  pounds. 

Regnault§  gives  for  the  weight  of  one  liter  of  mercury, 
13.5959  kilograms. 

*  Proceedings  of  the  Am.  Acad.  of  Arts  and  Sciences,  1882-83;  also  addi- 
tional observations. 

f  Proceedings  of  the  Royal  Society,  vol.  xv.     1866. 
%  Philosophical  Transactions,  cxlvi.      1856. 
§  Memoires  de  1'Institut  de  France,  vol.  xxi. 


SATURATED    VAPOR.  77 

The  degree  Fahrenheit  is  -|  of  the  degree  Centigrade. 
T  I-  *3-5959  X  2.204621 

JL/Ct  A?  —  a  > 

39-3702 

then  equations  B  and   C  have   for  the   reduction  to  degrees 
Fahrenheit,  and  pounds  on  the  square  inch, 

log/  =  a,  +  log  k  -  ba*»  +  cfi**  ; 
»  log p  —  a,  +  log  k  —  bjx*n  -f-  ^y^1* • 

The  resulting  equations  are  : 

B.  For  steam  from  32°  to  212°  F.  in  pounds  on  the  square 

inch, 

log  /  =  a^  —  ba*  +  eft*  ; 

a,  =  3-025908  ; 
log    b  —  0.6117400  ; 
log    c  —  8.13204  —  10  ; 
log  a^  —  9.998181015  —  10 ; 
log&  =0.0038134; 
n  =  t  —  32. 

C.  For  steam  from  212°  to  428°  F.  in  pounds  on  the  square 
inch, 

log  p  =  a,  —  b^a*  +  cJ3* ; 

a*  =  3- 743976  5 
log  bl  =  0.4120021  ; 

log  c,  =7.74168-  10 ; 
log  a^  =  9.998561831  —  10 ; 
log  A  =  0.0042454  ; 
n—  t  —  212. 

Other  Equations  for  the  Pressure  of  Steam. — Rankine* 
gives  the  following  equation  for  the  pressure  of  saturated  steam, 

/?        f* 
log/  =  ^--^-^=i, (107) 


*  Steam-engine  and  Other  Prime  Movers. 


78  THERMODYNAMICS  OF   THE  STEAM-ENGINE. 

in  which    T  is  the   absolute   temperature   calculated   by   the 
equation 

For  pounds  on  the  square  foot  the  values  of  the  constants  are 

A  =  8.2591  ;     log  B  =  343642  5     log  C  =  5-59873- 
For  pounds  on  the  square  inch  the  only  change  is 

A  =  6.1007. 

This  equation  has  the  advantage  that  it  may  be  solved 
directly  for  T,  a  property  that  Regnault's  equations  do  not 
have.  It  gives  quite  accurate  results,  and  the  greater  part  of 
English  tables  of  properties  of  saturated  steam  are  calculated 
by  its  aid.  The  following  table  will  give  a  comparison  between 
the  results  from  this  formula  and  those  from  formulae  B  and  C. 

RANKINE'S   EQUATION   FOR  STEAM. 


PRESSURE,  POUNDS  PER  SQUARE  INCH. 

TTTMPITT?  AT*TTT?T? 

(Fahrenheit). 

Regnault  at  45° 
latitude. 

Rankine. 

32° 

0.0890 

0.083 

77 

0-4555 

0.452 

122 

1.7789 

1.78 

I67 

5-579 

5.58 

212 

14.697 

14.70 

257 

33-7H 

33-71 

302 

69.27 

69.21 

347 

129.79 

129.8 

392 

225.56 

225.9 

428 

336-26 

336.3 

A  number  of  exponential  formulae  have  been  devised,  of 
which  the  principal  advantage  is  the  facility  of  application. 
The  following,  by  Magnus,  gives  pressures  in  mm.  of  mercury 
for  degrees  Centigrade,  and  agrees  quite  well  with  Regnault's 
results  below  100°,  but  is  not  so  correct  above  100° : 


7.4475  /___ 

4.525    X    I0234-69+'. 


(108) 


SATURATED    VAPOR.  79 

The  table  following  exhibits  the  defects  of  equation  (108) : 
MAGNUS'   EQUATION   FOR  STEAM. 


PRESSURES,  MM.  CF  MERCURY. 

(Centigrade). 

Regnault  at  45° 
latitude. 

Magnus. 

0° 

4.602 

4.525 

5° 

91.98 

91.97 

IOO 

760.0 

759-9 

150 

3581.9 

3627. 

200 

11664. 

12080. 

Pressure  of  Other  Vapors. — Regnault  *  determined  also 
the  pressure  of  a  large  number  of  saturated  vapors,  at  various 
temperatures,  and  deduced  equations  for  each  in  the  form  of 
equation  (94).  The  equations  and  the  constants  as  determined 
by  him  for  the  commoner  vapors  are  given  in  the  following  table  : 

PRESSURE   OF   SATURATED   VAPORS. 


log/ 

a 

b 

c 

Alcohol       

a  _  ba.n  4-  cfin 

5.4562028 

4  .  0800060 

0.0485397 

Ether      

a  4.  ban  —  cftn 

5.0286298 

0.0002284 

3  .  1906390 

Chloroform         .       .  . 

a  _  i,an  _  cfin 

5  .  22^^80^ 

2.0531281 

o.  0668673 

Carbon  bisulphide.  .  .. 
Carbon  tetrachloride.. 

a  —  ba*  —  cftn 

a  —  ban  _  cfin 

5.4011662 
12.0962331 

3.4405663 
9.1375180 

0.2857386 
1.9674890 

log  a 

log/3 

n 

Limits. 

Alcohol       

T  .00708557 

T.  040048  S 

t  -4-  2O 

—  20°,  -f-  150°  C. 

Ether  

0.0145775 

I.qq6877 

•/-f-  20 

—  2O°,  -f-  I2O°   C. 

Chloroform      

T   QQ74.I4.4. 

1.9868176 

t  —  2O 

4-  20°,  -1-  164°  C. 

Carbon  bisulphide.  .  .  . 
Carbon  tetrachloride.  . 

1.9977628 
I.9997I2O 

1.9911997 
1.9949780 

/4-  20 
t  -\-  20 

—  20°,  -fl400   C. 

-  20°,  4-  188°  C. 

*  Academic  des  Sciences,  Comptes  rendus,  Tome  xxxvi. 


8O  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Zeuner  *  states  that  there  is  a  slight  error  in  Regnault's  cal- 
culation of  the  constants  for  aceton,  and  gives  instead, 

log   /   —  a  —  ban  -f-  cfln  ; 

«=  5-3085419; 

\ogban  =  +  0.5312766  — 0.0026 1 48^; 
log  cfin  —  —  0.9645222  —  0.0215592^. 

Differential  Coefficient  ^.— From  the  general  form  of  the 
equation  (94),  we  have 


-cPn>  -    •    •   •   (109) 


M  being  the  modulus  of  the  common  system  of  logarithms. 
Differentiating, 


or,  reducing  to  common  logarithms, 


'- 


For  saturated  steam  at  45°  latitude,  the  constants  to  be 
used  with  equation  (i  10)  are  : 

*  Mechanische  Warmetheorie. 


SATURATED    VAPOR.  8  1 

French  units. 

B.  For  o°  to  100  C,  mm.  of  mercury, 

log  A  =  8.8512729—  10; 
log  B  =  6.69305  —  10  ; 
logal  =  9.996725828  —  10  ; 
=  0.0068641. 


C.  For  100°  to  220°  C.,  mm.  of  mercury, 

log^  =  8.5495158-10; 
log  £  =  6.  3493  1  —  10  ; 
log  a1  =  9.99741  1  296  —  10  ; 
log  /3l  =  0.00764  1  8. 

English  units. 

B.  For  32°  to  212°  F.,  pounds  on  the  square  inch, 

log  A  —  8.5960005  —  10; 
log  B  —  6.43778  —  10  ; 
logara  =  9.998181015  —  10; 
log  A  =  0.0038  1  34. 

C.  For  212°  to  428°  F.,  pounds  on  the  square  inch, 

log  A  =  8.2942434—  10  ; 
log  B  —  6.09403  —  10  ; 
logcx^  =  9.998561831  —  10; 
logA,=  0.0042454. 

It  is  to  be  remarked  that  -,-  may  be  found  approximately 
by  dividing  a  small  difference  of  pressure  by  the  corresponding 


82 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


Ap 
difference  of  temperature  ;  that  is,  by  calculating  — . 


With  a 


table  for  even  degrees  of  temperature,  we  may  calculate  the 
value  approximately  for  a  given  temperature  by  dividing  the 
difference  of  the  pressures  corresponding  to  the  next  higher  and 
t'he  next  lower  degrees  by  two. 

The   following   table  of   constants   for   the   several  vapors 
jviamed  were  calculated  by  Zeuner  from  the  preceding  equa- 
tions for  temperature  and    pressure  of  the  same  vapors  : 


DIFFERENTIAL  COEFFICIENT    -  -. 

p  dt 


SIGN. 

log(Aa.n) 

log  (Bpn) 

Aa» 

Bfi* 

1  1  1  1  1  + 

—     .1720041  —  0.0029143* 
—     .3396624  —  0.0031223* 
—     .3410130  —  0.0025856* 
—     -4339778  —  0.0022372* 
—     .8611078  —  0.0002880* 
—     .3268535  —  0.0026148* 

—  2.9992701  —  0.0590515* 
—  4.4616396  -}-  0.0145775* 
—  2.0667124  —  0.0131824* 
—  2.0511078  —  0.0088003* 
—  1.3812195  —  0.0050220* 
—  1.9064582  —  0.0215592* 

Ether 

Carbon  bisulphide  
Carbon  tetrachloride  

Heat  of  the  Liquid  and  Specific  Heat.— A  preliminary 
series  of  experiments  convinced  Regnault  that  the  specific  heat 
of  water  at  low  temperature  is  unity.  To  test  the  specific  heat 
at  higher  temperatures  he  ran  hot  water  from  a  boiler,  and  at 
a  known  temperature,  into  a  calorimeter  in  which  the  temper- 
ature varied  from  8°  to  14°  C.,  and  the  resulting  upper  temper- 
ature varied  from  17°  to  29°  C.  Knowing  the  original  weight 
of  water  in  the  calorimeter,  the  weight  run  in  from  the  boiler, 
and  the  initial  and  final  temperatures  in  the  calorimeter,  he 
calculated  the  mean  specific  heat  of  water  between  the  tem- 
perature of  the  boiler  and  the  final  temperatures  of  the  calo- 
rimeter. A  series  of  forty  such  experiments  was  made,  with 
the  temperature  of  the  boiler  varying  from  108°  to  192°  C., 
from  which  Regnault  concluded  that  the  mean  specific  heat 
from  o°  to  100°  is  1.005,  and  from  °°  to  2OO°,  1.016.  The  cor- 


SATURATED    VAPOR.  83 

responding  heat  of  the  liquid,  i.e.,  the  heat  required  to  raise  one 
kilogram  of  water  from  o°  to  a  given  temperature,  /,  is  : 


For  100°,     ....     100.5  i 
"    200°,     ....     203.2. 

Assuming  an  equation  of  the  form 

9  =  t  +  Af  +  £f,. (in) 

and  solving  for  the  two  constants  by  aid  of  the  two  known  values 
of  q,  the  following  equation,  which  is  commonly  used,  is  deduced  : 

g  =  t  +  0.00002/2  +  0.0000003  A    .     .     .     (112) 
The  specific  heat  at  any  temperature  is,  therefore, 


dq 
=  ~    =  i  +  O.OOOO4/  -f-  0.0000009**.    .     (113) 


These  equations  are  for  use  with  the  Centigrade  scale  ;  for 
the  Fahrenheit  scale,  a  given  temperature  may  be  reduced  to 
the  Centigrade  scale,  and  then  introduced  in  the  same  equations. 

The  process  of  making  the  experiments  is  really  a  complex 
one  ;  for  the  water  in  leaving  the  boiler  has  work  done  on  it  by 
the  steam  pressure  in  the  boiler,  and  it  has  a  certain  velocity 
impressed  on  it  at  the  same  time,  and  again,  in  entering  the 
calorimeter,  it  does  work  against  the  atmospheric  pressure,  and 
the  kinetic  energy  of  its  motion  is  changed  into  heat.  At 
higher  temperatures  there  is  a  double  change  of  state  ;  part  of 
the  water  changes  to  steam  on  leaving  the  boiler,  and  that 
steam  is  condensed  again  in  the  calorimeter.  It  is  probable 
that  the  error  of  neglecting  the  effect  of  these  several  actions 
is  inconsiderable. 


84  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  degree  of  accuracy  to  be  accorded  to  this  work  is  in- 
dicated by  the  fact  that  Regnault  gives  four  significant  figures 
in  stating  the  data  for  the  calculation  of  the  constants  in  the 
equations. 

Similar  experiments  were  made  to  determine  the  heat  of 
the  liquid  of  other  volatile  liquids,  the  results  of  which  were  as 
follows : 

HEAT   OF   THE   LIQUID. 
Alcohol q  —  o.54754/-{- 0.0011218/2 

-f-  O.OOOOO22O6/3. 

Ether t q  —  0.52901/4-  0.0002959^. 

Chloroform q  =  o.23235/-|~°- 0000507^. 

Carbon  bisulphide q  =  o. 23523* -f-  o.ooooSis/2. 

Carbon  tetrachloride q  =  0.19798*-}-  o.  0000906**. 

Aceton q  —  o.  50643* -j-o.  0003965  *2. 

The  specific  heat  at  any  temperature  may  be  obtained  by  dif- 
ferentiating the  equations  for  the  heat  of  the  liquid,  thereby 
obtaining  equations  like  equation  (113). 

Rowland's  Experiments. — A  series  of  experiments  was 
made  by  Rowland  *  at  Baltimore  to  determine  the  mechanical 
equivalent  of  heat,  which  gave  a  delicate  method  of  determin- 
ing the  heat  of  the  liquid  and  the  specific  heat. 

The  apparatus  used  was  similar  to  that  used  by  Joule,  with 
modifications  to  give  greater  certainty  of  results.  The  calo- 
rimeter was  of  larger  size,  and  the  paddle  had  the  upper  vanes 
curved  like  the  blades  of  a  centrifugal  pump,  to  give  a  strong 
circulation  up  through  the  centre,  past  the  thermometer  for 
taking  the  temperatures,  and  down  at  the  outside.  The  paddle 
was  driven  by  a  petroleum  engine,  and  the  power  applied  was 
measured  by  making  the  calorimeter  into  a  friction  brake,  with 
two  arms  at  which  the  turning  moment  was  measured.  Radia- 
tion was  made  as  small  as  possible,  and  then  was  made  deter- 
minate by  use  of  a  water-jacket  outside  of  the  calorimeter. 

The  experiments  consisted  essentially  in  delivering  a  meas- 

*  Proceedings  of  the  American  Academy,  vol.  xv.  (N.  S.  vii.).     1879. 


SATURATED    VAPOR. 


ured  amount  of  work  to  the  water  in  the  calorimeter,  and  in 
noting  the  rise  of  temperature  produced  thereby. 

The  whole  range  covered  by  the  experiments  was  from  2° 
to  41°  C.  The  results  show  that  430  kilogrammeters  of  work 
are  required  to  raise  one  kilogram  of  water  from  2°  to  3°  C. 
Assuming  that  the  same  amount  will  be  required  to  raise  the 
same  weight  from  o°  to  i°,  and  from  i°  to  2°,  the  following 
table  has  been  arranged  from  Rowland's  final  table  of  results  : 

ROWLAND'S   MECHANICAL   EQUIVALENT   OF   HEAT. 


u 

IB! 

£3 

"rtJJ    • 

•123 

J*l 

2s  i 

13 
£U    . 

£ri 

U 

i>! 

Jz  w  bfl 

•si  - 

i!3 

41 

i 
£<->  . 
£•2  "8 

£ 

-jS.2 

.g'lpj 

S|| 

*j3 

w 

~*22 

Til 

o  3  ti 
4-.  crJS 

V 

o'oS 

8  MS 

rt-:  « 

OJi—  1   O. 

or-;  3 

4JI—  1  O 

B 

1^5 

^w"© 

S3& 

rt-^  3 

VM  O 

Q 

H 

E 

53 

Q 

h 

SB 

X 

pa 

I 

2 

3 

4 

5 

I 

2 

3 

4 

5 

I 

Q 

I.  0068 

i  007 

22 

2 

4.26.  i 

22.065 

22.063 

2 

860 

2.0135 

A  •  \j\j  y 

2  .014 

27 

08  <o 

*T^ 
426.O 

27.  06^ 

23.061 

3 

1290 



3.0204 

3'.O22 

*o 

24 

Vw  j^ 

10277 

*§••*'  "  ** 

**^>  .  v^^J 

24.062 

24-059 

* 

1721 

4  .0295 

4O2Q 

2  C 

10701 

AOZ        A 

2  c    (~)C  e 

2  c  ocft 

5 

•  /** 
2I5O 

429.8 

5.0339 

.  V  '—     * 

5.036 

26 

11128 

425.7 

26.054 

26.053 

6 

2580 

429.  5 

6  .  0408 

6.040 

27 

11553 

425.6 

27.050 

27.048 

7 

3009 

429.3 

7-0452 

7-045 

28 

11978 

425.6 

28.045 

28.042 

8 

3439 

429.0 

8.0520 

8.049 

29 

12399 

425.5 

29.031 

29.037 

9 

3868 

428.8 

9-0564. 

9-054 

30 

12828 

425.6 

30.035 

30.032 

10 

4296 

428.5 

10.059 

10.058 

31 

13253 

425.6 

31.030 

31.027 

ii 

4723 

428.3 

11.058 

I  I  .  060 

32 

13675 

425-6 

32.018 

32.023 

12 

428.1 

12.061 

12.061 

33 

14101 

425.7 

33.016 

33.018 

13 

5578 

427.9 

13.060 

13.063 

34 

14527 

34-on 

34.014 

14 

6006 

427.7 

14-063 

14.064 

35 

14952 

425.8 

35.008 

35.009 

15 

6433 

427.4 

15.065 

15.066 

36 

15379 

425.8 

36.008 

36.007 

16 

6861 

427.2 

16.064 

16.066 

37 

15805 

37.007 

37.005 

17 

7289 

427.0 

i  7  .  066 

i  7  .  066 

38 

16231 



38.003 

38.004 

18 

7717 

426.8- 

18.068 

18.066 

39 

16657 



39.000 

39  .  002 

19 

8144 

426.6 

19.068 

19.066 

40 

17083 

39-998 

40.000 

20 

8571 

426.4 

20.068 

20  .  066 

41 

17508 

4O.QQ3 

21 

8997 

426.2 

21.065 

21.064 

*TW  *  77  3 

In  the  above  table,  column  I  gives  the  number  of  degrees 
above  freezing  on  the  Centigrade  scale ;  column  2  gives  the 
number  of  kilogrammeters  required  to  raise  one  kilogram  of 
water  from  freezing-point  to  the  given  temperature ;  column  3 
is  Rowland's  mechanical  equivalent  of  heat  at  the  given  tem- 
perature derived  from  10°  intervals  on  column  2  ;  column  4  is 
obtained  by  dividing  the  numbers  in  column  2  by  the  mechani- 


86  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

cal  equivalent  of  heat  at  i6|°  C.,  or  62°  F.,  from  column  3  ;  and 
column  5  is  calculated  by  considering  the  specific  heat  to  be 
constant  for  each  five  degrees  of  temperature.  These  specific 
heats  were  derived  from  a  curve  obtained  by  plotting  tempera- 
tures for  abscissae,  and  heats  of  the  liquid  for  ordinates.  The 
values  of  the  specific  heats  will  be  given  later  in  connection 
with  those  for  higher  temperatures. 

A  review  of  the  preceding  table  shows  that  the  specific  heat 
at  low  temperatures  varies  quite  markedly,  so  that  it  appeared 
advisable  to  investigate  the  effect  of  this  variation  on  Regnault's 
experiments  already  quoted.  This  was  done  quite  expeditiously 
by  multiplying  the  mean  specific  heat  given  by  him  for  his 
several  experiments  by  the  true  average  specific  heat  for  the 
range  of  temperature  in  the  calorimeter.  This  corrected  specific 
heat  was  then  used  to  calculate  the  increase  of  heat  from  the 
final  temperature  of  the  calorimeter  to  the  temperature  of  the 
boiler,  and  that  increase  was  added  to  the  heat  of  the  liquid 
from  the  table  to  find  the  heat  of  the  liquid  at  the  temperature 
of  the  boiler.  The  results  were  then  plotted  as  before,  and 
compared  with  the  heats  of  the  liquid  derived  from  Regnault's 
mean  specific  heats  uncorrected.  The  points  by  the  corrected 
method  were  a  little  more  regularly  arranged  than  the  points 
obtained  by  assuming  the  specific  heat  to  be  unity  at  low  tem- 
peratures ;  but  the  improvement  was  inconsiderable.  The  in- 
equality of  the  specific  heat  at  low  temperatures  is  seldom  so 
much  as  the  unavoidable  errors  of  the  method. 

It  appeared  that  if  the  specific  heat  was  assumed  to  be  con- 
stant, from  40°  to  45°,  from  45°  to  155°,  and  from  155°  to 
200°  C.,  the  straight  lines  thus  drawn  represented  the  experi- 
mental values  as  recalculated  quite  nearly ;  and  further,  they 
represented  the  uncorrected  experimental  values  more  nearly 
than  Regnault's  equation. 

Specific  Heat  of  Water. — The  combination  of  Rowland's 
and  Regnault's  experiments  on  the  heat  of  the  liquid  by  the 
method  described  gives  the  specific  heats  set  down  in  the  fol- 
lowing table : 


SATURATED    VAPOR. 

I 

SPECIFIC    HEAT   OF   WATER. 


RANGE. 

Specific  Heat. 

Centigrade. 

Fahrenheit. 

o  to       5 

32    to     41 

1.0072 

5   to     10 

41    to     50 

I  .  0044 

10  to     15 

50  to     59 

I.  OOl6 

15  to     20 

59  to     68 

I. 

20  to     25 

68  to     77 

0.9984 

25    to     30 

77  to     86 

0.9948 

30  to     35 

86  to     95 

0.9954 

35   to     40 

95   to  104 

0.9982 

40  to     45 

104  to  113 

I. 

45   to  155 

113   to  311 

1.008 

155   to  200 

311   to  392 

1.046 

Standard  Temperature. — In  the  beginning  of  our  work  it 
was  stated  that  we  should  use  62°  F.  for  our  standard  tempera- 
ture ;  and  the  reasons  for  so  doing  may  now  be  shown.  We 
know  actually  nothing  about  the  specific  heat  of  water  from 
o°  to  2°  C. ;  consequently,  the  commonly  accepted  value  of  the 
thermal  unit,  z>.,  the  heat  required  to  raise  one  unit  of  weight 
of  water  from  o°  to  1°  C.,  or  from  32°  to  33°  F.,  is  an  ideal 
quantity  inferred  from  the  behavior  of  water  at  higher  tem- 
peratures. It  is  more  scientific  to  take  an  easily  verified 
quantity  for  the  standard  ;  and  there  is  a  practical  convenience 
in  choosing  62°  F.  for  the  standard  temperature,  because  it  is 
near  the  mean  temperature  of  the  air  during  experimental 
work.  Therefore,  it  is  near  the  mean  temperature  in  the  calo- 
rimeter during  ordinary  work  with  that  instrument ;  and  the 
specific  heat  of  water  for  the  range  of  temperature  in  the  calo- 
rimeter may  usually  be  considered  to  be  unity,  without  error, 
unless  great  refinement  is  desired. 

Mechanical  Equivalent  of  Heat. — The  mechanical  equiv- 
alent in  meter-kilograms  of  one  calorie  at  i6f°  C.,  deduced  from 
Rowland's  experiments  in  the  third  column  of  the  table  on 
page  85,  15427.1. 

Since  the  value  given  by  Joule  is  commonly  quoted,  it  will 
be  of  interest  to  make  a  comparison  of  his  latest  work  (1873) 
with  Rowland's,  as  given  in  the  following  table : 


88  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

0 

COMPARISON   OF   ROWLAND'S   AND   JOULE'S    EXPERIMENTS. 


Reduced  to  the  Air  Thermometer 

TEMPERATURE. 

Joule's  Value  at 
Manchester, 
English  System. 

and  to  the  latitude  of  Baltimore. 

Rowland's  Value, 
Corresponding. 

English. 

French. 

14°.  7 

772.7 

776.1 

425.8 

427.6 

12°.  7 

774.6 

778.5 

427.1 

428.0 

15°.  5 

773-1 

776.4 

426.0 

427.3 

I4°-  5 

767.0 

770.5 

422.7 

427.5 

I7°-  3 

774.0 

777-0 

426.3 

426.9 

The  value  of  g  at  Baltimore,  latitude  39°  17',  is  980.05 
centimeters  ;  therefore,  reducing  to  45°  of  latitude  and  at  the 
sea  level,  the  value  of  J  is 


or,  as  it  has  been  given  before, 

/  =  426.9. 

To  reduce  to  the  English  system,  multiply  by  -|,  and  by  the 
length  of  the  meter  in  feet,  so  that 

/=778. 

Total  Heat.  —  This  term  is  defined  as  the  heat  required  to 
raise  a  unit  of  weight  of  water  from  freezing-point  to  a  given 
temperature,  and  to  entirely  evaporate  it  at  that  temperature. 
The  experiments  made  by  Regnault  were  in  the  reverse  order  ; 
that  is,  steam  was*  led  from  a  boiler  into  the  calorimeter  and 
there  condensed.  Knowing  the  initial  and  final-  weights  of  the 
calorimeter,  the  temperature  of  the  steam,  and  the  initial  and 
final  temperatures  of  the  water  in  the  calorimeter,  he  was  able, 
after  applying  the  necessary  corrections,  to  calculate  the  total 
heats  for  the  several  experiments. 


SATURATED    VAPOR.  89 

As  a  conclusion  of  the  work  he  gives  the  following  values 
for  the  total  heats  : 

10°,     .     .     .     610     By  equation,  609.6 
63°,     ...     625  625.2 

100°,     ...     637 
195°,     ...     666 

Assuming  an  equation  of  the  form 

1i  =  A+£tt (114) 

Regnault  calculated  the  constants  from  the  values  given  for 
100°  and  195°,  and  gives  the  equation 

A  =  606.5  +  0.305^ (115) 

In  order  to  see  the  effect  of  the  varying  value  of  the  specific 
heat  at  low  temperatures,  the  total  heats  given  by  experiment 
were  recalculated  by  a  method  resembling  that  used  in  recalcu- 
lation of  the  heats  of  the  liquid,  and  the  results  plotted  to- 
gether with  Regnault's  values  uncorrected.  The  recalculated 
points  were  a  little  more  regular  than  the  original  ones,  and  lay 
nearer  the  line  represented  by  the  equation  (115).  Especially 
did  the  recalculated  points  for  those  experiments,  for  which  the 
true  mean  specific  heat  of  the  water  in  the  calorimeter  was 
nearly  unity,  lie  near  that  line.  It  therefore  appears  that 
equation  (115)  represents  our  best  knowledge  of  the  total  heat 
of  steam. 

For  the  Fahrenheit  scale  the  equation  becomes 

A  =  1091.7  +  0.305  (/  — 32) (116) 

Regnault  gives  the  equations  following  for  other  liquids : 

Ether A  =    94     +0.45^        —  o.  00055556/2 

Chloroform A—    67      +0.1375^. 

Carbon  bisulphide A  =    90     -f-o.  14601^  —  0.0004123^ 

Carbon  tetrachloride A  =    52      -f-  o.  14625^  — •'0.000172^ 

Aceton A  =  140.5  -|-o.36644/  —  0.000516 f 

Heat  of  Vaporization.— If  the  heat  of  the  liquid  be  sub- 
tracted from  the  total  heat,  the  remainder  is  called  the  heat 
of  vaporization,  and  is  represented  by  r,  so  that 

r  =  \-q (117) 


9o 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


Specific  Volume  of  Liquids. — The  coefficient  of  expan- 
sion of  most  liquids  is  large  as  compared  with  that  of  solids, 
but  it  is  small  as  compared  with  that  of  gases  or  vapors. 
Again,  the  specific  volume  of  a  vapor  is  large  compared  with 
that  of  the  liquid  from  which  it  is  formed.  Consequently  the 
error  of  neglecting  the  increase  of  volume  of  a  liquid  with  the 
rise  of  temperature  is  small  in  equations  relating  to  the  ther- 
modynamics of  a  saturated  vapor,  or  of  a  mixture  of  a  liquid 
and  its  vapor  when  a  considerable  part  by  weight  of  the  mix- 
ture is  vapor.  It  is  therefore  customary  to  consider  the  spe- 
cific volume  of  a  liquid  a  to  be  constant. 

Experiments  were  made  by  Hirn  *  to  determine  the  volumes 
of  liquid  at  high  temperatures  compared  with  the  volume  at 
freezing-point,  by  a  method  which  was  essentially  to  use  them 
for  the  expansive  substance  of  a  thermometer.  The  results 
are  given  in  the  following  equations : 

SPECIFIC  VOLUMES  OF   HOT  LIQUIDS. 


Water, 

100°  C.   to  200°  C. 

(Vol.  at  4°  =  unity.) 


Logarithms. 

v  =  i-f-  o.oooio867875/  {6.0361445  —  10 

-j- 0.0000030073653^  14.4781862  —  10 

-j-  0.000000028730422^         11.4583419  —  10 

—  0.0000000000066457031^8.8225409  —  20 


Alcohol, 

v  =  i  +  0.00073892265^        6.8685991  —  10 

30°  C.  to  1  60°  C. 

4-  0.00001055235^       3.0233492  —  10 

(Vol.  at  o°  —  unity.) 

—  0.000000092480842^    12.9660517  —  10 

+  0.00000000040413567^  0.6065278  —  10 

Ether, 

v  —  I  -f-  0.0013489059^         7.1299817  —  10 

30°  C.  to  130°  C. 

-f  0.0000065  5  37^ 

4.8164866  —  10 

(Vol.  at  o°  =  unity.) 

—  o.  0000000344907  s6*3 

2.5377028  —  10 

-f-  0.00000000033772062^ 

0.5285571  —  10 

Carbon  Bisulphide, 

v  =  i  -j-  0.0011680559^ 

7.0674636  —  10 

30°  C.  to  i6oc  C. 

-j-  0.0000016489598^ 

4.2172103  —  10 

(Vol.  at  o°  =  unity.) 

—  0.0000000008  1  1  igo62/3 

0.9091229  —  lo 

-f-  0.000000000060946589^ 

9.7849494  —  20 

Carbon  Tetrachloride, 

v  =  i  -f-  o.ooio67i883/ 

7.0282409  —  10 

30°  C.  to  160°  C. 

-j-  0.000003565  1  378/2 

4.5520763—  10 

(Vol.  at  o°  =  unity.) 

—  0.00000001494928  1/3 

2.1746202  —  10 

-f-  O.OOOOOOOOOO85I823I8/4 

9.9303494  —  20 

*Annales  de  Chimie  et  de  Physique,  1867. 


SATURATED    VAPOR. 

Internal  and  External  Latent  Heat.  —  The  heat  of  vap- 
orization overcomes,  external  pressure,  and  changes  the  state 
from  liquid  to  vapor  at  constant  temperature  and  pressure.  Let 
the  specific  volume  of  the  saturated  vapor  be  s,  and  that  of  the 
liquid  be  <r,  then  the  change  of  volume  is  s  —  <r  =  u,  on  pass- 
ing from  the  liquid  to  the  vaporous  state.  The  external  work  is 


(118) 


and  the  corresponding  amount  of  heat,  or  the  external  latent 
heat,  is 

Ap(s—<r)  =  Apu  ......     (119) 

The  heat  required  to  do  the  disgregation  work,  or  the  in- 
ternal latent  heat,  is 

p  =  r  —  Apu  .......     (I2°) 

Specific  Heats  of  Water  and  Steam.  —  In  the  general 
discussion  of  thermodynamics  and  the  application  to  gases  two 
kinds  of  specific  heat  were  used,  at  constant  volume  and  at 
constant  pressure.  In  dealing  with  solids  and  with  liquids  be- 
low the  boiling-point  the  only  specific  heat  that  has  been 
determined  is  the  specific  heat  at  constant  pressure  :  for  exam- 
ple, the  specific  heat  of  water  determined  from  Rowland's  ex- 
periments is  of  that  sort.  For  most  solids  and  liquids  the 
specific  heat  at  constant  volume  cannot  be  very  different  from 
the  specific  heat  at  constant  pressure,  and  it  is  commonly 
assumed  that  they  are  identical. 

If  a  given  substance  experience  a  change  of  temperature 
under  a  specific  condition,  then  the  heat  required  to  change  the 
temperature  of  a  unit  of  weight  one  degree  is  the  specific  heat 
under  that  condition.  There  will,  therefore,  be  as  many  kinds 
of  specific  heat  as  there  are  conditions.  In  dealing  with  a  mix- 
ture of  a  liquid  and  its  vapor,  for  which  the  pressure  is  a  func- 
tion of  the  temperature  only,  the  specific  heat  for  each  is  defined 
under  the  condition  that  the  pressure  shall  vary  with  the  tem- 
perature, according  to  the  law  of  saturated  vapor  given  by  the 
general  equation  (94). 


92  THERMODYNAMICS  OF  THE   STEAM-ENGINE. 

Let  c  be  the  specific  heat  of  water  under  the  given  condi- 
tions. The  meaning  may  be  deduced  from  equation  (6)  applied 
to  pure  liquid, 


dQ  dp 


For  water  we  may  use  q,  the  heat  of  the  liquid,  for  Q,  and 
then 

dq  dp 


The  only  reason  for  writing  the  last  equation  is  to  give  a 
clearer  conception  of  the  subject,  for  no  experimental  work  exists 
for  its  use.  Regnault's  experiments  probably  give  c  rather  than 
cp .  In  any  case  no  attempt  is  made  in  thermodynamics  to  dis- 
tinguish between  the  different  kinds  of  specific  heat  for  water. 

The  specific  heat  of  saturated  steam,  i.e.,  the  heat  that  must 
be  given  to  one  unit  of  weight  of  steam,  when  the  temperature 
is  raised  one  degree  and  the  pressure  raised  the  corresponding 
amount,  in  order  that  the  steam  shall  remain  dry  and  satu- 
rated, is  represented  by  h.  An  equation  having  the  form  of 
equation  (121)  cannot  be  employed,  since  the  temperature  can- 
not be  raised  without  raising  the  pressure  at  the  same  time. 
An  investigation  of  other  properties  of  steam  will  determine 
the  form  and  value  of  this  function. 

General  Equation. — A  pound  or  a  kilogram  of  a  mixture 
of  a  liquid  and  its  vapor  consists  of  a  certain  part,  x,  of  vapor, 
and  the  remainder,  I  —  x ,  of  liquid.  The  specific  volume  of 
the  mixture  is 

V  =  XS  +  (l   —  X}<?  =  (S  —  <J)X  -\-  <J  =  UX  -\-  (T.     .       (122) 


SATURATED    VAPOR.  93 

When  a  mixture  of  liquid  and  a  vapor  receives  heat,  there 
is  in  general  an  increase  of  temperature  of  each  component, 
and  a  change  of  part  of  the  liquid  into  vapor. 


.  •  .  dQ  =  hxdt  +  c(i  —  x)dt  +  rdx.      .     .     (123) 

Application  of  the  First  Law.  —  Proceeding  as  we  have 
in  our  preceding  work,  equations  (24)  and  (r2^)  give        (  •*.  3 


dQ  =  A(dE  +pdv)  —  hxdt  +  c(\  —  x]dt  +  rdx  ; 
dE  =  ~  \hx-\-  c(i  -  x}\  dt^-^dx  -pdv. 


But 


Since 


dxdt  '    dtdx  ' 

d 


Bearing  in  mind  that  k,  c,  and  p  are  functions  of  t  and  not 
of  x,  the  differentiation  gives 


I  /^r\         /^>\   /dfe;\  d*v 

-^\dt)x~  \4tlMx)  t~P'dtd~x 


* 

94  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

But 

<Tv  __d*v          ,    ldp\         dp  _     ,   ldr\         dr 


dxdt      dtdx 


ldp\         dp  idr\         dr 

and   (T.      = -j-  and   KJ    =  -r; ; 
VK/  «W  w  ^ 


From  equation  (122),  cr  being  constant, 


..  _=. 


(124) 


Application  of  the   Second   Law.  —  By  this  law  -~  is  a 
perfect  differential. 


dQ       hx  +  c(\  -  x)  J         r  J 
'»  ~=  -  f.^+.^R     .     .    (125) 


h  —  c  _       dt 
T  ~I 


dr   ,  r 

~   +  C-h= (I27) 


SATURATED    VAPOR.  95 

First  and  Second  Laws  Combined. — The  combination 
of  equations  (124)  and  (127)  gives 


; ("8) 

IV» 

Specific  Heat  of  Steam.— Equation  (127)  solved  for  h  gives 


Now  r  =  A  —  q  —  606.5  +  0.305*  —  q, 

and  q  calculated  by  the  aid  of  the  table  on  page  87  will  have 
for  its  value 

q  =  const.  +  c(t  —  const.); 
hence  we  shall  have 


dr 

-     =0.305  —c\ 


=:  0.305   — (130) 


The  term  -~  may  be  calculated  by  aid  of  equation  (115)  and 

:ie  table  on  page  87,  and  then  the  following  values  of  h  may 
be  calculated  by  equation  (130) : 

SPECIFIC  HEAT  OF  STEAM. 

o°  C.          50°  C.        100°  C.         150°  C.        200°  C. 
h=—  1.911,  --  1.461,   —  1.131,  —0.879,  —0.676. 


96  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  negative  sign  shows  that  heat  must  be  abstracted  from 
saturated  steam  when  the  temperature  and  pressure  are  increased, 
otherwise  it  will  become  superheated.  On  the  other  hand, 
steam,  when  it  suddenly  expands  with  a  loss  of  temperature 
and  pressure,  suffers  condensation,  and  the  heat  thus  liberated 
supplies  that  required  by  the  uncondensed  portion. 

Him*  verified  this  conclusion  by  suddenly  expanding  steam 
in  a  cylinder  with  glass  sides,  whereupon  the  clear  saturated 
steam  suffered  partial  condensation  as  indicated  by  the  forma- 
tion of  a  cloud  of  mist.  The  reverse  of  this  experiment  showed 
that  steam  does  not  condense  with  sudden  compression,  as 
shown  by  Cazin. 

Ether  has  a  positive. value  for  h.  As  the  theory  indicates, 
a  cloud  is  formed  during  sudden  compression,  but  not  during 
sudden  expansion. 

The  table  of  values  of  h  for  steam  shows  a  notable  decrease 
for  higher  temperatures,  which  indicates  a  point  of  inversion 
at  which  h  is  zero  and  above  which  h  is  positive,  but  the  tem- 
perature of  that  point  cannot  be  determined  by  our  own  ex- 
perimental knowledge.  For  chloroform  the  point  of  inversion 
was  calculated  by  Cazinf  to  be  I23°.48,  and  determined  experi- 
mentally by  him  to  be  between  125°  and  129°.  The  discre- 
pancy is  mostly  due  to  the  imperfection  of  the  apparatus  used, 
which  substituted  finite  changes  of  considerable  magnitude  for 
the  indefinitely  small  changes  required  by  the  theory. 

Specific  Volume  and  Density. — Solving  equation  (128) 
for  u,  we  have 


dt 

which  gives  a  method  of  calculating  the  increase  of  volume 


*  Bulletin  de  la  Societe  Industr.  de  Mulhouse,  cxxxiii. 
f  Comptes  rendus  de  1'Academie  des  Sciences,  Ixii. 


SATURATED    VAPOR.  97 

due  to  vaporization  from  experimental  data.  The  specific 
volume  s  and  density  y  are  thus  known  from  the  equations 

s-u-i-  cr,    .     .     . (132) 

y  =  j.      ....    .fc.    ...    (133) 

It  is  of  interest  to  consider  the  degree  of  accuracy  that  may 
be  expected  from  this  method  of  calculating  the  density  of 
saturated  vapor.  The  value  of  r  depends  on  A.  and  q  ;  for  the 
first  Regnault  gives  three  figures  in  the  data  from  which  the 
empirical  equation  is  deduced,  and  the  experimental  work  does 
not  indicate  a  greater  degree  of  accuracy.  The  fourth  figure, 
if  stated,  is  likely  to  be  in  error  to  the  extent  of  five  units. 
The  value  of  T  is  commonly  stated  in  four  figures,  of  which 
the  last  may  be  in  error  by  two  units,  A,  as  determined  by 
Rowland,  has  four  figures,  the  last  being  uncertain  4;o  the  ex- 
tent of  one  or  two  units.  The  differential  coefficient  —.  is 

at 

deduced  from  the  equations  for  calculating/;  and  those  equa- 
tions are  derived  from  data  havmg  five  places  of  significant 
figures.  Now  each  of  the  equations  B  and  C,  for  steam  at  45° 
latitude  for  the  English  system,  gives  a  pressure  of  14.6967 
pounds  on  the  square  inch ;  but  the  specific  volume  calculated 
by  aid  of  equation  B  is  26.550  cubic  feet,  while  equation  C 
gives  26.637  cubic  feet.  The  mean,  26.60,  differs  from  either 
extreme  by  about  one  in  seven  hundred.  This  discrepancy- is 
due  to  the  fact  that  the  curves  represented  by  equations  B  and 
C  meet  at  the  common  temperature,  212°,  but  do  not  have  a 
common  tangent.  Since  the  equations  are  empirical  and  not 
logical,  the  errdr  or  uncertainty  is  unavoidable,  and  all  cal- 
culated specific  volumes  are  affected  by  a  similar  uncertainty. 
The  greatest  probable  error  is  in  determining  r,  for  which  it 
may  be  about  one  in  one  thousand.  The  error  introduced  into 
this  equation  by  using  the  values  of  A  in  common  use,  that  is, 
772  instead  of  778,  is  about  one  in  one  hundred. 

The  specific  volume  and  density  are  commonly  calculated 


98  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

in  the  method  given,  on  account  of  the  great  difficulty  of  the 
experimental  determination,  and  the  error  of  the  method  is 
not  greater  than  that  of  the  other  parts  of  steam  tables. 

Tate  and  Fairbairn's  Experimental  Determination. — 
The  great  uncertainty  of  the  direct  determination  of  the 
density  of  saturated  vapor  is  due  to  difficulty 
of  determining  when  steam  is  dry  and  satu- 
rated. A  small  quantity  of  liquid  present,  or  a 
slight  degree  of  superheating,  will  introduce 
serious  errors.  Fig.  26  is  an  ideal  representa- 
tion of  the  saturation  gaug*  used  by  Tate  and 
Fairbairn*  in  their  experiments  to  determine 
this  point.  A  and  B  are  globes  in  which  there  is  steam  with  a 
small  quantity  of  water,  having  a  communication  by  means  of 
a  tube  partially  filled  with  mercury.  The  globes  and  tubes  are 
immersed  in  a  bath  by  which  all  may  be  raised  to  any  given 
temperature.  So  long  as  any  water  exists  in  both  globes  the 
pressure  in  both  will  be  the  same,  and  the  mercury  will  be  at 
the  same  level  in  both  legs  of  the  tube.  As  the  tempera- 
ture rises  the  water  in  the  globes  will  be  gradually  vaporized, 
till  all  in  A,  containing  the  l^ast  amount,  is  changed  into  steam. 
At  this  instant  the  steam  in  A  is  dry  and  saturated,  and  if  the 
weight  and  volume  are  known  the  density  can  be  found.  As 
the  process  goes  on  the  steam  in  A  becomes  superheated,  and, 
the  pressure  being  less  than  for  saturated  steam  at  the  same 
temperature,  the  mercury  at  a  will  rise. 

In  making  the  experiments  it  was  found  advisable  to  super- 
heat the  steam  in  A  and  then  to  let  the  temperature  gradually 
fall,  and  to  take  a  series  of  readings  of  the  difference  in  height 
of  a  and  b  simultaneously  with  the  readings  of  the  thermom- 
eter in  the  bath,  from  which  the  temperature  could  be  inferred 
at  which  the  steam  became  saturated.  At  the  same  time  the 
steam  pressure  was  taken  by  a  mercury  column.  The  actual 
apparatus  had  a  different  appearance,  and  was  arranged  for 
convenience  in  observation,  and  had  two  forms,  one  for  pres- 
sures above  that  of  the  atmosphere,  and  one  for  pressures  below. 

*  Philosophical  Transactions,  vol.  cl.     1860.      . 


SATURATED    VAPOR. 


99 


The  following  table  gives  a  summary  of  all  of  the  experi- 
ments made.  The  second  and  third  columns  give  the  pressure 
and  temperature  of  saturation;  the  fourth  gives  the  relative 
volume  compared  with  water ;  the  fifth  gives  the  same  volume 
by  an  empirical  formula ;  and  the  sixth  gives  the  proportional 
error  of  the  formula  compared  with  the  experimental  value. 

TATE  AND  FAIRBAIRN'S   EXPERIMENTAL  DETERMINATION    OF 
THE   DENSITY   OF   SATURATED   STEAM. 


Pressure  in 
Inches  of 
Mercury. 
P 

Maximum 
Temperature 
of  Saturation. 

Specific 
Volume  from 
Experiment. 
V 

Specific 
Volume  from 
Formula. 
V 

Error  of 
Formula. 

I 

5-35 

136.77 

8275-3 

8183 

-A 

2 

8.62 

155-33 

5333.5 

5326 

T  ~$~S 

3 

9-45 

159-36 

4920.2 

4900 

-»ii 

4 

12.47 

170.92 

3722.6 

3766 

-f"*V 

5 

12.  6l 

171.48 

37I5.I 

3740 

+  rb" 

6 

13.62 

174.92 

3438.1 

3478 

+  A 

7 

16.01 

182.30 

3051.0 

2985 

-*v 

8 

18.36 

188.30 

2623.4 

2620 

+  ¥TT 

9 

22.88 

198.78 

2149-5 

2124 

-& 

i' 

53.61 

242.90 

943-1 

937 

-T^T 

2' 

55.52 

244.82 

908.0 

906 

T§T 

3' 

55-89 

245-22 

892.5 

900 

~T~  TTT 

4' 

66.84 

255-50 

759-4 

758 

5' 

76.20 

263.14 

649    2 

669 

+  ^V 

6' 

81.53 

267.21 

635.3 

628 

_  ^ 

7' 

84.20 

269.20 

605.7 

608 

+  3¥¥ 

8' 

92.23 

274.76 

584.4 

562 

_  ^ 

9' 
10' 

90.08 

99.60 

273.30 
279.42 

543-2 
515.0 

545 
519 

+  **T 

n' 

104.54 

282.58 

497.2 

496 

_  -^ 

12' 

112.78 

287.25 

458.3 

461 

+  ii* 

13' 

122.25 

292.53 

433-1 

428 

—  ^ 

14' 

114.25 

288.25 

449.6 

456 

•+-A 

The  formula  deduced  by  the  experimenters  to  represent 
their  work  is 


034) 


100 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


in  which  V  is  the  volume  of  steam  compared  with  the  volume 
of  the  water  from  which  it  was  produced,  and  P  is  the  pressure 
in  inches  of  mercury. 

Although  the  experiments  were  made  with  great  care  and 
all  precautions  were  taken  to  avoid  error,  the  results  are  less 
satisfactory  than  those  obtained  by  calculation  from  the  other 
known  properties  of  steam. 

To  show  the  comparison  between  the  values  of  the  specific 
volume  determined  by  the  two  methods,  the  following  table 
has  been  calculated  for  English  units : 

SPECIFIC  VOLUME  OF  SATURATED  STEAM. 


Pressure, 

Specific  Volume,  Cubic  Feet  per  Pound. 

Pounds  per  Square 
Inch. 

j_     r      dt 

v     _r6_  j     49513 

S~AT'dp 

5 

73-2 

73-2 

15 

26.2 

25-8 

25 

16.1 

15.8 

35 

II-  7 

11.4 

45 

9-3 

9.0 

55 

7-7 

7-5 

Zeuner's    Equation    for    Internal    Latent    Heat. — To 

avoid  the  laborious  calculation  of  this  quantity  by  the  exact 
methods,  Zeuner  has  proposed  the  following  simple  empirical 
equations  for  that  purpose  in  the  French  system : 

INTERNAL  LATENT  HEAT. 

Water p  =  575.40  —  0.791* 

Ether p  =    86.54  —  0.10648*  —  0.0007160^ 

Chloroform p  =    62.44  —  o.  11282*  —  0.0000140^ 

Carbon  bisulphide p  =    82.79  —  0.11446*—  o. 0004020^ 

Carbon  tetrachloride p  =    48.57  — '0.06844*  —  o.ooo2oSo/2 

Aceton p  =  131.63  —  0.20184*  —  0.0006280** 

The    following   table    shows  that   the   equation   for  water 
gives  a  fair  degree  of  approximation  : 

0°  50°  100°  150°  200° 

By  equation  (i  20).... 575.5     536.3     496.4     457.4     417.4 

By  empirical  equation 5754     535-9    496.3     456.8     417.1 


SATURATED    VAPOR.  IOI 

Critical  Temperature.  —  The  empirical  equation,  and  also 
the  value  of  p  in  the  table  above  by  the  exact  method,  show 
that  the  internal  latent  heat  decreases  as  the  temperature  rises, 
and  at  sufficiently  high  temperatures  it  will  approach  zero.  If 
p  is  made  zero  in  Zeuner's  equation  for  water,  the  corre- 
sponding temperature  is  720°  C,  which  indicates  that  the  true 
point  is  much  beyond  the  limits  of  experiments. 

The  temperature  at  which  p  becomes  zero  for  any  vapor  is 
called  the  critical  temperature,  for  at  that  temperature  the  dis- 
tinction between  the  liquid  and  its  vapor  vanishes,  and  above 
that  temperature  the  vapor  or  gas  cannot  be  liquefied  by  pres- 
sure alone.  It  has  been  proposed  to  call  a  substance  which  is 
above  the  critical  temperature  a  gas,  and  one  which  is  below  a 
vapor. 

Experiments  on  liquids  strongly  heated  in  strong  glass 
tubes  show  that  vaporization  proceeds  gradually  as  the  tem- 
perature rises,  until  a  temperature  is  reached  at  which  the  line 
of  demarcation  between  the  liquid  and  its  vapor  becomes  indis- 
tinct. Above  that  temperature  the  liquid  all  disappears,  and 
the  tube  is  full  of  gas.  This  is  the  critical  temperature. 
Avenarius*  by  this  method  determined  the  critical  tempera- 
ture of  four  liquids.  He  also  selected  from  Regnault's  experi- 
ments the  data  most  applicable,  and  from  them  deduced 
equations  like  those  given  by  Zeuner  for  the  internal  latent 
heat  of  vapors,  and  calculated  the  critical  temperature  by  their 
aid.  The  results  are  as  follows  : 

Experimental.          Calculated. 

Ether  .........  .  .............  196°.  2  C.  I96°.8  C. 

Carbon  bisulphide  ............  276°.  I  274°.o 

Carbon  tetrachloride  ..........  292°.$  298°.? 

Aceton  ...............  ,  ......  246°.  I  230°.  4 

Effect  of  Pressure  on  Change  of  State.  —  If  equation 
(128)  be  solved  for  the  differential  of  the  pressure  with  regard 
to  temperature, 

dp  _      r 


*  Poggendorffs  Annalen,  cli.     1874. 


102  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

in  which  A  and   T  are  positive,  and  r  is  positive  below 

dp 
critical  temperature.     Consequently  •£•  is  positive  or  negative, 

according  as  s  is  greater  or  less  than  cr.     When  ~  is  positive, 

an  increase  of  pressure  causes  a  rise  of  the  temperature  of  the 
change  of  state,  and  vice  versa. 

The  application  of  the  foregoing  to  the  formation  of  steam 
only  confirms  what  we  already  know,  that  the  temperature  of 
boiling-point  increases  with  the  pressure.  But  an  application 
to  the  melting  of  ice  is  of  more  interest.  To  make  the  appli- 
cation, let  s  represent  the  specific  volume  of  water,  and  cr  that 
of  ice,  the  latter  being  larger  than  the  former.  In  this  case  u  is 

dp 
negative,  and  -j-  is  also  negative,  showing  that  an  increase  of 

pressure  lowers  the  melting-point,  a  fact  that  has  been  proved 
by  experiment,  and  which  is  used  in  explaining  regelation. 

Curve  of  Constant  Steam  Weight. — It  was  formerly 
assumed  in  the  theory  of  the  steam-engine  that  the  interchange 
of  heat  between  the  steam  and  the  iron  of  the  cylinder  was  by 
radiation  ;  and  further,  that  the  condensation  accompanying 
adiabatic  expansion  formed  a  cloud  which  instigated  a  rapid  in- 
terchange of  heat,  where  before  little  had  occurred.  The  steam- 
jacket  was  assumed  to  impart  just  heat  enough  to  dissipate 
this  cloud  and  keep  the  steam  dry.  Hence  the  curve  of  dry 
saturated  steam  was  of  great  importance  in  the  theory  of  the 
steam-engine,  and  it  is  sometimes  drawn  on  indicator  cards 
instead  of  the  hyperbola.  The  substitution  has  no  good 
reason,  for  the  curve  is  not  a  better  approximation  to  the 
curve  drawn  by  an  indicator,  and  is  more  troublesome  to  con- 
struct. 

The  action  of  steam  in  the  engine  cylinder  has  been  proved 
to  be  quite  different,  for  the  interchange  of  heat  is  caused  by 
condensation  by  contact  of  the  steam  with  the  iron,  or  by 
evaporation  of  moisture  from  it,  and  the  curve  of  saturated 
steam  no  longer  plays  an  important  part  in  the  theory  of  the 


SATURATED    VAPOR.  103 

steam-engine.     Still  it  is  of  importance  as  forming  the  bound- 
ary-line between  superheated  steam  and  wet  steam. 

The  curve  may  be  represented  very  closely  by  an  expo- 
nential formula  resembling  that  deduced  for  the  adiabatic  line 
for  a  perfect  gas ;  i.e., 

pvn  =  pp?  =  const (i  36) 

Rankine  proposed  the  value  ^J  for  the  exponent  n,  and 
Zeuner  has  found  that  1.0646  gives  still  a  closer  approximation. 
The  actual  curve  may  be  drawn  by  plotting  pressures  and 
volumes  from  a  table  of  the  properties  of  saturated  steam. 

Exponential    Equation. — To   find   the   exponent   of   an 
equation   representing  a  curve  passing  through  two  points,  #0 
and  tfj ,  Fig.  27,  take  logarithms  of  both  sides 
of  equation  (136),  and  we  have 

n  log  v  -{-  log  p  =  n  log  vl  -\- 
logA  —  log/ 


-  log*-- log  < 

Isothermal  Lines. — Since  the  pressure  of  saturated  vapor 
is  a  function  of  the  temperature  only,  the  isothermal  line  of  a 
mixture  of  a  liquid  and  its  vapor  is  a  line  of  equal  pressures, 
parallel  to  the  axis  of  volumes.  Steam  expanding  from  the 
boiler  into  the  cylinder  of  an  engine  follows  such  a  line ;  that 
is,  the  steam  line  of  an  automatic  cut-off  engine  with  ample 
ports  is  nearly  parallel  to  the  atmospheric  line. 

The  heat  required  for  an  increase  of  volume  at  constant 
pressure  is 


(138) 


which  may  be  obtained  by  integrating  equation  (123)  with  the 
assumption  that  the  temperature  is  constant,  or  it  may  be 
written  directly,  since  r  is  the  heat  of  vaporization,  and  x^  —  x^ 
is  the  weight  of  liquid  vaporized. 


104  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  work  done  by  the  vapor  during  such  an  expansion  is 
W  =  p(vt-vl)=pu(xt-xl).      .     .     .     (139) 

Isodynamic  or  Isoenergic  Lines.  —  The  following  method 
of  treating  the  isodynamic  changes  of  a  mixture  of  a  liquid 
and  its  vapor  is  due  to  Zeuner,  and  is  similar  to  his  method  of 
treating  adiabatic  changes.  It  does  not  give  an  equation  to 
the  curve  of  pressures  and  volumes,  but  it  gives  the  solution  of 
all  problems  that  arise. 

The  increase  of  intrinsic  energy  of  the  mixture  of  a  liquid 
and  its  vapor,  above  freezing-point,  is 


040) 


The  change  of  intrinsic  energy  in  passing  from  one  condition^ 
to  another  is 


^2  —  EI  =  -£  fe  —  &  +  *.  P2  -  *A).    •     .     (141) 

When   the  change  is  isodynamic,  the  energy  remains  the 
same  by  definition,  and 


*iPi  =  o  ;  ......    (142) 

which  equation,  together  with  the  formulae 

v*  =  *,«,  +  0;       v,  =  x,u,  +  <7,       .     .     .     (143) 

gives  the  means  of  solving  all  problems. 

For  example,  suppose  that  the  initial  and  final  pressures  are 
given,  to  find  the  corresponding  volumes  ;  then,  xl  being  also 
known,  x^  may  be  found  from  equation  (142),  and  then  the 
volumes  may  be  found  by  equations  (143).  On  the  other  hand, 
if  the  volumes  are  given  and  the  pressures  are  required,  the 
problem  can  be  solved  only  by  approximations. 

Assume  a  probable  value  p9'  for  the  final  pressure,  and  cal- 


SATURATED    VAPOR.  IO5 

culate  the  corresponding  value  of  vj.  From  the  comparison  of 
v^  and  vj  assume  a  second  approximate  value  /„",  and  calculate 
z/a",  and  repeat  the  process  till  a  sufficiently  close  approxima- 
tion is  attained.  For  the  first  approximation  it  will  commonly 
be  convenient  to  assume  that  the  pressures  are  inversely  pro- 
portional to  the  volumes. 

The  direct  determination  of  the  heat  required  and  of  the 
external  work  done  by  the  mixture  of  liquid  and  vapor  during 
an  isodynamic  expansion  would  require,  for  convenient  work, 
the  calculation  of  special  empirical  formulae  or  of  the  tables 
equivalent  to  them  ;  which  is  not  justified  by  the  importance 
of  the  subject.  An  approximate  solution  may  be  had  by  aid  of 
an  exponential  formula  determined  from  the  initial  and  final 
pressures  and  volumes  ;  and  since  the  curve  represented  by  such 
a  formula  agrees  quite  well  with  the  actual  expansion  curve, 
the  approximation  is  sufficient  for  the  solution  of  problems. 

Suppose  we  have  the  formula 

pvn  =  pp?  =  const.  ; 
then 

Q  =  AW=Ajpdv,  .....     (144) 

since  the  heat  received  is  all  changed  into  external  work,  the 
intrinsic  energy  remaining  constant. 

Zeuner  states  that  n  is  1.0456  when  the  steam  is  dry  and 
saturated  at  the  initial  state. 

Entropy  of  a  Mixture  of  a  Liquid  and  its  Vapor.— 
From  the  second  law  of  thermodynamics, 


in  which  0  is  the  entropy,  dQ  is  the  heat  transmitted,  and  T  is 
the  absolute  temperature.  Since  the  entropy  depends  only  on 
the  state  of  a  substance,  and  not  on  the  method  of  arriving  at 
that  state,  the  increase  of  entropy  of  one  unit  of  weight  of  a 
given  mixture  of  a  liquid  and  its  vapor,  above  the  entropy  of 


106  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

one  unit  of  weight  of  that  liquid  at  freezing-point  of  water, 
may  be  calculated  in  the  following  method  : 

Suppose  that  one  unit  of  weight  of  a  liquid  be  raised  from 
freezing-point  to  the  temperature  /,  and  that  a  portion  x  be  then 
changed  into  vapor.  During  the  first  operation  the  increase  of 
entropy  will  be 

/*  dq          pt  cdt 

=  Jo      ~T=Jo      T> 

and  during  the  second  operation  the  increase  will  be 


xr 
7" 

since  the  heat  is  added  at  a  constant  temperature  t  during  that 
operation.     The  entire  increase  of  entropy  will  be 

*  cdt 


xr         pt  cat  _xr 

T  +  J0  Y"':T 


For  any  other  state  determined  by  xl  and  tl  we  shall  have, 
for  the  increase  of  entropy  above  that  of  liquid  at  freezing-point, 

x  r 
11    i    ft 

TT  +  '" 

The  change  of  entropy  in  passing  from  one  state  to  another 
is 

3£f  3£  ¥ 

0_0i  =  — +  0--^'+^.     .    .    .    (145) 

Entropy  of  the  Liquid. — When  the  specific  heat  of  a  liquid 
is  known  in  terms  of  the  temperature,  the  entropy  of  the  liquid 
is  readily  calculated.  Thus,  for  ether,  the  equation  is 

8  =  I     (0.52901  +  0.0059 1 8/W 


SATURATED    VAPOR.  IO/ 

The  form  of  the  equation  for  the  entropy  of  water  is  more 
easily  stated  for  a  special'  case.     For  example,  at  13°  C,  it  is  . 

T  T  T 

1.0072  'log,  ~r  +  1.0044  log,  ^  +  I.OOI6  log,—-*  —  0.04663. 

<*<>  -1  5  •*•  0 

Adiabatic    Equation    for  a    Liquid  and    its    Vapor.  — 

During  an  adiabatic  change  the  entropy  is  constant,  so  that 
equation  (145)  gives 


(I46> 


When  the  initial  state,  determined  by  xl  and  ^  or  /,  ,  is 
known  and  the  final  temperature  fa  ,  or  the  final  pressure  /„  , 
the  final  value  x^  may  be  found  by  equation  (146).  The  initial 
and  final  volumes  may  be  calculated  by  the  equations 

vl  =  xlr1  -\-  &     and     vz  =  x^r^  -)-  cr. 

Tables  of  the  properties  of  saturated  vapors  commonly  give  the 
specific  volume  s,  but 

s  —  u  -\-  cr. 

Problems  in  which  the  initial  condition  and  the  final  tem- 
perature or  pressure  are  given,  may  be  solved  directly  by  aid 
of  the  preceding  equations.  Those  giving  the  final  volume  in- 
stead of  the  temperature  or  pressure  can  be  solved  only  by 
approximations.  An  equation  to  an  adiabatic  curve  in  terms  of 
/  and  v  cannot  be  given,  but  such  a  curve  for  any  particular 
case  may  be  constructed  point  by  point. 

Clausius  and  Rankine  independently  and  at  about  the  same 
time  deduced  equations  identical  with  equations  (145)  and  (146), 
but  by  methods  each  of  which  differed  from  that  given  here. 

If  tables  giving  #,  the  entropy  of  the  liquid,  are  not  at  hand, 
an  approximate  result  may  be  obtained  by  considering  the 
specific  heat  c  to  be  a  constant,  so  that 


fed*  _       fdt  _  T, 

—  J  ~T  —  cj~r  — c  log* -7^-; 


IOS  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

or  equation  (146)  may  be  written, 

^•  =  ^  +  log.£  .....    .    .    .    :    (147) 

J-  a  J.  l  J.  a 

In  the  discussion  of  the  specific  heat  h  of  a  saturated  vapor, 
it  appeared  that  the  expansion  of  dry  saturated  steam  in  a  non- 
conducting cylinder  would  be  accompanied  by  partial  conden- 
sation. The  same  fact  may  be  brought  out  more  clearly  at 
this  place.  One  pound  of  dry  steam  at  100  pounds  absolute 
pressure  will  have  the  values 


58  F.,     r,  =  884.0,     6,  =  o.4733>     fi  =.t 
If  the  final  pressure  is  15  pounds  absolute,  we  have 
3  F.,     ra  =  965.1,     0,1=0.3143; 


whence 

884.0 


,  =  0.8133. 


On  the  other  hand,  h  is  positive  for  ether,  and  partial  con- 
densation takes  place  during  compression  in  a  non-conducting 
cylinder.  For  example,  let  the  initial  condition  be 

tl  =  10°  C.,       ^  —  93.12,     0,  =  0.0191,     xl  =  I, 
and  let  the  final  conditions  be 

^  =  120°  C.,     ry  =  72.26,     03  =  0.2045, 


then 


03.12    ,  72.26^ 

0.0191  =  ^-     --2-+ 0.2045; 


283-7  393-7 

and  x^  =  0.724.  ^ 

Equation  (146)  applies  to  all  possible  mixtures  of  a  liquid 
and  its  vapor,  including  the  case  of  xl  =  o  or  the  case  of  liquid 


SATURATED    VAPOR. 


I09 


without  vapor,  but  at  the  pressure  corresponding  to  the  tem- 
perature according  to  the  law  of  saturated  vapor.  When 
applied  to  hot  water,  this  equation  shows  that  an  expansion  in 
a  non-conducting  cylinder  is  accompanied  by  a  partial  vapor- 
ization. 

There  is  some  initial  state  of  the  mixture  such  that  the 
value  of  x  shall  be  the  same  at  the  beginning  and  at  the  end, 
though  it  may  vary  at  intermediate  states.  To  find  that  value 
make  x^  =  x^  in  equation  (146)  and  solve  for  xl ,  which  gives 


The  value  of  xl  to  fulfil  the  conditions  given  varies  with  the 
initial  and  final  temperatures  chosen,  but  in  any  case  it  will  not 
be  much  different  from  one  half.  It  may  therefore  be  generally 
stated  that  a  mixture  of  steam  and  water,  when  expanded  in  a 
non-conducting  cylinder,  will  show  partial  condensation  if  more 
than  half  is  steam,  and  partial  evaporation  if  more  than  half 
water.  If  the  mixture  is  nearly  half  water  and  half  steam,  the 
change  must  be  investigated  to  determine  whether  evaporation 
or  condensation  will  occur ;  but  in  any  case  the  action  will  be 
small. 

Construction  of  Adiabatic  Lines. — In  case  a  series  of 
adiabatic  lines  is  to  be  drawn,  the  following  method  may  be 
used  with  advantage.  In  Fig.  28 
draw  the  line  BB  parallel  to  OP,  P 
the  axis  of  P,  making  OB  =  <r,  so 
that  BB  represents  the  volume  of 
one  kilogram  of  water  at  all  tem- 
peratures and  pressures.  At  the 
point  O,  which  represents  the  high- 
est pressure  to  be  used,  draw 
OD  —  ul ,  corresponding  to  the  FlG-  28< 

given  pressure  ;  then  D  represents  the  condition  when  the  mix- 
ture is  all  dry  saturated  steam;  i.e.,  x  —  I,  v  =  s.     Though  not 


110  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

essential  to  the  solution  of  the  problem,  it  is  interesting  to  draw 
the  line  of  saturated  steam  DD,  which  forms  a  boundary  be- 
tween moist  steam  and  superheated  steam  ;  a  point  to  the  left 
of  DD,  or  between  that  line  and  BB,  represents  a  mixture  of 
water  and  steam,  and  a  point  to  the  right  of  DD  represents 
superheated  steam. 

The  points  O  and  D  represent  the  two  extreme  cases,  pure 
water  and  dry  steam  ;  and  the  point  xl  ,  between  O  and  D,  repre- 
sents a  mixture  of  water  and  steam.  Equation  (154)  gives  for 
a  pressure  p  the  following  expressions  for  XQ  ,  x,  and  x'  ',  corre- 
sponding to  the  initial  conditions  O,  x^  ,  and  D  or  x  =  i  : 

*-f+0  =  0,;  .......    (149) 

XY  y  Y 

-T+-0  =  -^  +  ei;      ....     (I50) 

•*  i 

^  +  o  =  ^  +  0>  .....    (150 

*  i 

Subtracting  in  succession  equation  (149)  from  (150)  and 
(151),  we  have 

(  \  -          •  !*-• 

\X          XQ)    ~  ,   —  %\   'j*    '•> 


X  —  XQ 


Designating  the  final  volumes  by  v0,  v,  and  v',  we  have 

Z>0  =  XJA  +  CT,       V  =  XU  -\-  <T,       V'  =  X'U  -\-  CT  ; 

v-v0_x-x0_ 

'  ^r^;-yz.T0-  *"   ••   •   •   (153) 

.  • .  v  =  x,  (v'  -  v0)  +  v, (154) 


SATURATED    VAPOR.  Ill 

Now  calculate  x9  and  x'  with  the  corresponding  values  of  VQ 
and  £\  in  the  usual  method,  and  calculate  v  by  the  equation 
(154),  and  complete  Fig.  28  by  plotting  the  points  #0,  x,  and  x' 
on  the  line  x^x'  at  a  distance  VQXO  from  0z/,  equal  to  the  pres- 
sure/. 

The  equations  (149),  (151),  and  (154)  are  true  for  any  press- 
sure  / ;  for  example,  the  pressure  represented  by  the  dotted 
line  on  Fig.  28,  so  that  a  sufficient  number  of  points  may  be 
located  and  the  three  curves  o*\ ,  xjc,  and  Dx'  may  be  drawn. 

Thus  far  it  appears  that  the  labor  of  constructing  the  inter- 
mediate curve  xjc  directly  by  the  usual  method  would  be  less, 
but  an  advantage  will  be  given  by  the  new  method  when  a 
large  number  of  intermediate  curves  corresponding  to  different 
initial  values  of  x  are  to  be  drawn;  equation  (153)  will  then 
give  the  several  values  of  x  with  great  rapidity.  Fig.  28  is  also 
useful  in  giving  a  comprehensive  idea  of  the  action  of  various 
mixtures  of  water  and  steam  in  a  non-conducting  cylinder,  the 
proportions  being  as  nearly  correct  as  can  be  represented  by  a 
figure  of  the  size. 

External  Work  during  Adiabatic  Expansion. — Since  no 
heat  is  transmitted  during  an  adiabatic  expansion,  all  of  the 
intrinsic  energy  lost  is  changed  into  external  work,  so  that,  by 
equation  (141), 


The  adiabatic  curve  cannot  be  well  represented  by  an  ex- 
ponential equation ;  for  if  an  exponent  be  determined  for  such 
a  curve  passing  through  points  representing  the  initial  and  final 
states,  it  will  be  found  that  the  exponent  will  vary  widely  with 
different  ranges  of  pressure,  and  still  more  with  different  initial 
values  of  x ;  and  that,  further,  the  intermediate  points  will  not 
be  well  represented  by  such  an  exponential  curve,  even  though 
it  passes  through  the  initial  and  final  points. 

This  fact  was  first  pointed  out  by  Zeuner,  who  found  that 
the  most  important  element  in  determining  n  was  x^ ,  the  ini- 
tial condition  of  the  mixture.  He  gives  the  following  empirical 


112  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

formula  for  determining  n,  which  gives  a  fair  approximation  for 
ordinary  ranges  of  temperature  : 

^=1.035+0.100^.     .     .     .     .     .     (156) 

Rankine*  proposed  the  exponential  formula 

=  const. 


for  the  expansion  of  saturated  steam  in  a  lagged  cylinder  with- 
out a  steam-jacket. 

It  is  probable  that  this  equation  was  obtained  by  comparing 
the  expansion  lines  on  a  large  number  of  indicator  diagrams. 
It  corresponds  nearly  with  the  true  adiabatic  line  for  x^  ,  the 
initial  value  at  cut-off,  equal  to  0.80.  This  equation  has  been 
largely  used  in  England  on  account  of  the  esteem  in  which 
Rankine's  work  is  held  ;  and  as  he  does  not  state  its  origin,  it 
appears  to  have  been  regarded  as  the  true  adiabatic  line  for  a 
steam-engine. 

There  does  not  appear  to  be  any  good  reason  for  using  an 
exponential  equation  in  this  connection,  for  all  problems  can  be 
solved  accurately  by  the  method  given,  and  the  action  of  a 
lagged  steam-engine  cylinder  is  far  from  being  adiabatic.  An 
adiabatic  line  drawn  on  an  indicator  card  is  instructive,  since  it 
shows  to  the  eye  the  difference  between  the  expansion  in  an 
actual  engine  and  that  of  an  ideal  non-conducting  cylinder;  but 
it  can  be  intelligently  drawn  only  after  an  elaborate  engine 
test.  For  general  purposes  the  hyperbola  is  the  best  curve  for 
comparison  with  the  expansion  curve  of  an  indicator  card,  for 
the  reason  that  it  is  the  conventional  curve,  and  is  near  enough 
to  the  curve  of  the  diagrams  from  good  engines  to  allow  a  prac- 
tical engineer  to  guess  at  the  probable  behavior  of  an  engine, 
from  the  card  alone.  It  cannot  in  any  sense  be  considered  as 
the  theoretical  curve. 

EXAMPLES. 

I.  Calculate  the  pressure,  heat  of  the  liquid,  total  heat, 
heat  of  vaporization,  specific  volume,  etc.,  at  several  tempera- 

*  Steam-engine  and  Other  Prime  Movers. 


SATURATED    VAPOR.  113 

tures  for  the  vapors  for  which  the  data  and  equations  are  given, 
and  compare  with  results  given  in  the  Tables  of  the  Properties 
of  Saturated  Steam. 

2.  Find   the  exponent    for  an    exponential  curve   passing 
through  the  points/  =  30,  v  =  1.9,  and/,  =  15,  v  —  9.6. 

3.  Find  the  exponent  for  a  curve  to  pass  through  the  points 
/  —  40,  v  =  2,  and/!  =  12,  vl  =  6. 

4.  In  examples  2  and  3,  let  p  be  the  pressure  in  pounds 
on  the  square  inch,  and  v  the  volume  in  cubic  feet ;  find  the 
external  work  of  expansion  in  each  case. 

5.  Find  the  external  work  of  expansion  of  a  fluid,  following 
the  law  given  by  the  equation  ptf ,  which  has  the  initial  volume 
3  cubic  meters,  and  the    initial  pressure  4  atmospheres,  and 
which  expands  till  the  pressure  becomes  one  atmosphere. 

6.  A  pound  of  steam  and  water  at  1 50  pounds  pressure  is 
O.6  steam  ;  what  is  the  increase  of  entropy  above  that  of  water 
at  32°  F.  ? 

7.  A  kilogram  of  chloroform  at  100°  C.  is  0.8  vapor ;  what  is 
the  increase  of  entropy  above  that  of  the  liquid  at  o°  C.  ? 
Apply  to  other  vapors  for  which  data  are  given. 

8.  The  initial  condition  of  a  mixture  of  water  and  steam  is 
/  =  320°  F.,  x  =  0.8 ;  what  is  the  final  condition  after  adiabatic 
expansion  to  212°  F.  ?     Solve  with  the  following  values  for  x\ 
0.9,  0.6,  0.4,  0.3,  o.o. 

9.  The  initial  condition  of  a  mixture  of  steam  and  water  is 
p  =  3000  mm.,  x  =  0.9 ;  find  the  condition  after  an  adiabatic 
expansion  to  600  mm.     Apply  to  other  vapors  for  which  data 
are  given. 

10.  A  cubic  foot  of  a  mixture  of  water  and  steam,  x  =  0.8, 
is  under  the  pressure  of  60  pounds  by  the  gauge.     Find  its 
volume  after  it  expands  adiabatically  till  the  pressure  is  reduced 
to  10  pounds  by  the  gauge  ;  also  the  external  work  of  expansion. 

n.  A  test  of  an  engine  with  the  cut-off  at  0.106  of  the 
stroke,  and  the  release  at  0.98  of  the  stroke,  and  with  4.5  per 
cent  clearance,  gave  for  the  pressure  at  cut-off  62.2  pounds  by 
the  indicator,  and  at  release  6.2  pounds ;  the  mixture  in  the 
cylinder  at  cut-off  was  0.465  steam,  and  at  release  0.921  steam. 


114  THERMODYNAMICS  OF  THE   STEAM-ENGINE. 

Find  (i)  condition  of  the  mixture  in  the  cylinder  at  release  on 
the  assumption  of  adiabatic  expansion  to  release ;  (2)  condition 
of  mixture  on  the  assumption  of  hyperbolic  expansion,  or  that 
pv=plv^1  (3)  the  exponent  of  an  exponential  curve  passing 
through  points  of  cut-off  and  release ;  (4)  exponent  of  a  curve 
passing  through  the  initial  and  final  points  on  the  assumption 
of  adiabatic  expansion ;  (5)  the  piston  displacement  was  0.7 
cubic  feet,  find  the  external  work  under  exponential  curve 
passing  through  the  points  of  cut-off  and  release;  also  under  the 
adiabatic  curve. 


CHAPTER   VIII. 

SUPERHEATED    STEAM. 

A  DRY  and  saturated  vapor,  not  in  contact  with  the  liquid 
from  which  it  is  formed,  may  be  heated  to  a  temperature 
greater  than  that  corresponding  to  the  given  pressure  for  the 
same  vapor  when  saturated.  Such  a  vapor  is  said  to  be  super- 
heated. When  far  removed  from  the  temperature  of  satura- 
tion, such  a  vapor  follows  the  laws  of  perfect  gases  very  nearly, 
but  near  the  temperature  of  saturation  the  departure  from 
those  laws  is  too  great  to  allow  of  calculations  by  them  for  en- 
gineering purposes. 

In  the  case  of  superheated  steam  various  provisional  char- 
acteristic equations  have  been  proposed  for  use  until  the  neces- 
sary experimental  investigation  shall  give  the  data  for  a  true 
theory.  The  theory  given  here  was  proposed  by  Zeuner.  It 
is  convenient  for  calculation  and  appears  to  give  good  results. 

Substituting  in  the  characteristic  equation  for  a  gas 

pv  =  RT, 
the  value  of  R  from  equation  (61)  gives 


The  form  of  characteristic  equation  proposed  by  Zeuner  for 
superheated  steam  is 

*-'       -       ~-  058) 


Il6  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  specific  heat  at  constant  pressure  cp  is  assumed  to  be 
constant,  k  is  a  constant  suggested  by  the  ratio  K  of  the  specific 
heats  of  a  gas  ;  but  it  will  be  shown  that  the  specific  heat  at 
constant  volume,  determined  from  the  equation  (158),  is  a 
variable,  consequently^  cannot  be  the  ratio  of  the  specific  heats 
of  superheated  steam.  C  and  a  are  constants  that  are  to  be 
determined  from  the  known  properties  of  saturated  and  super- 
heated steam. 

Partial  differentiation  of  equation  (158)  gives 

'dt\  Apk 


dt\  Avk          aJ^AkC 

dl-    Ck-  Ck-    I       ' 


Cp(k-     |);  Cp(k- 

Application  of  the  First  Law.  —  The   application  of  the 
first  law  of  thermodynamics  by  aid  of  equation  (48), 


i(tdo\          tdn\    )    _ 
4  (  \dplv       \dvlf)   ' 


A 

gives  another  form  for  (-7-).    Substituting  for  o  and  n  in  terms 
of  the  specific  heats  gives 


dp  dv 

Substituting  the  value  of  (—  )  from  equation  (159),  and  per 

\dv  I  p 

forming  the  differentiation  indicated, 


Ak 


••-<«« 


SUPERHEATED   STEAM.  II? 

Integration  gives 

dt  Av 


Application  of  the  Second  Law.  —  Equation  (55), 


deduced  by  the  successive  application  of  the  two  laws  of  ther- 
modynamics, can  be  most  conveniently  used  in  this  place. 
Substituting  the  values  of  the  partial  differential  coefficients 
from  equations  (159)  and  (163)  gives 

(k  -  i)'    T 


which  gives  the  method  of  calculating  the  specific  heat  at  con- 
stant volume  when  cp  and  k  are  known. 

Value  of  the  Exponent  a.  —  Equating  the  values  of  the 
differential  coefficient  given  by  equations  (160)  and  (163), 
Av  Avk  apa-*AkC 

+ 


cv(k-i)~  cp(k-i)       cp(k-i)' 

Substituting  for  C  from  equation  (158),  and  for  c,  from  (164), 
we  have 

Av      r  (k  -  i)a       T\  _       Avk 


apa-*Ak  rcf     k  -  I      T         v 

r        _ 


Av        ,   k—  i      T          Avk  T  a  Avk 

T         T\  ~T~        r        •  ~T"  —  T7A T\    i  a  ~~L  7~Z         I 

/^  —  IJ             /^            p          cp\&  —  v  P  ^A     —  ^ 

^—  i    r     ^ _    r     ^z/  £ 


/      ^  '^-i' 

.   (165) 


Il8  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Characteristic  Equation.— Substituting  the  value  deduced 
for  a  in  equation  (158)  gives,  for  the  characteristic  equation  for 
superheated  steam, 


Pv  =       'y     •   T-Cp—.     .     .    .-  .     (166) 

Thermal  Capacities.— From    equations  (11),   (159),   and 
(164), 


~C\cv       l}\dv)p-CvC>       k     ~  '  Apv  '  cp(k  -  i) ; 

T 
.'.    l  =  Cv(k-i)- (167) 

V 

From  equations  (15),  (163),  and  (164), 

'dt\   --ccyLL-jLL     JL          Av 

v  p       k.       '  Apv  '  cv(k  —  i)  ' 

k-  i  T 


(168) 


From  equations  (17)  and  (160), 
'dt\          Apk 


From  equations  (18)  and  (163), 
fdt\  Av 


General  Equations.  —  Substituting  the  values  of  /,  m,  n, 
and  o  in  equations  (5),  (6),  and  (7)  give,  for  the  general  equations 
for  superheated  steam, 


dQ=         c,dt  +  (k-l)<iv;       .     .     (171) 

.dp\;       .     .     (172) 
(173) 


SUPERHEATED   STEAM.  1  19 

It  is  instructive  to  compare  these  equations  with  the  gen- 
eral equations  (70),  (71),  and  (72)  for  perfect  gases,  which  may 
be  written, 


dQ=        c,dt  +  (K-i)dv;      .     .  (174) 

dQ=--       cp\dt-   K-^--jdp\;     .    .  (i75) 

dQ  =  -^-\vdp  +  Kpdv\.     ....  (176) 

K  ~~~  I    \  } 


To  obtain  equation  (176),  equation  (72)  may  be  written, 


~ 


_ 

^ 


c  -  c       c  - 


It  is  to  be  remarked  that  equation  (174)  is  not  useful  in  its 
present  form,  since  cv  is  a  variable,  but  it  is  written  for  symme- 
try in  comparison  with  equations  (174),  (175),  and  (176). 

Entropy.  —  Equation  (172)  gives 

dt       k-id 


-,     .     (178) 


which  is  to  be  compared  with  equation  (85)  for  gases.  Equa- 
tions in  terms  of  v  and  /,  or  p  and  v  may  be  deduced,  which 
will  also  have  the  same  form  as  those  for  gases. 

Value  of  k.  —  The  characteristic  equation  for  superheated 
steam  is  intended  to  apply  to  all  degrees  of  superheating,  ap- 
proaching, at  one  limit,  the  condition  of  a  gas,  and  at  the  other, 


I2O  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

that  of   saturated  vapor.     For  a  mixture  of   a  liquid  and  its 
vapor  we  have,  from  equation  (145), 


or,  for  saturated  steam  with  x  =  i, 


~ 


=  ~  (cdt  +  dr-~  dty  .     (179) 


Equations  (177)  and  (179)  should  both  be  true  for  dry  sat- 
urated steam,  whence 

k  -  i      T     dp 


T     dp\  dr        r 

---dt)  =  c+---  •  • 


By  equation  (127)  the  right-hand  member  of  equation  (180) 
is  equal  to  h,  the  specific  heat  of  saturated  steam  ;  consequently 

k-i_       cp-h 


Numerical  Values.  —  Regnault  gives  as  the  results  of  three 
experiments  on  the  specific  heat  of  superheated  steam  at  con- 
stant pressure 

0.48111,         0.48080,         0.47963, 

and  for  the  mean  value 

cp  —  0.4805. 

With  this  value  of  cp  and  the  known  values  of  the  other 
factors,  determined  from  the  properties  of  saturated  steam,  the 
following  values  of  k  were  calculated  : 

Pressure,  pounds  ) 
on  the  sq.  in.     \  2O°         3OO 

k  1.335       1-332       1-330       1.324 


SUPERHEATED   STEAM.  121 

Zeuner  assumed  for  the  constant  k  the  value 

£  =  £=1.333+, (l82) 

which  may  be  compared  with  the  ratio  of  the  specific  heats  of 
air, 

K  =    1.405. 

With  this  assumed  value  of  k  and  the  known  values  of  A 
and  Cp  the  coefficient  of  T  in  the  characteristic  equation  (166) 
becomes: 

French  system,         -—  — -7—  =  B  —  5 1.28  ; 
English  system,        -~  — y —  =  B  =  93.46. 

./A  K 

The  specific  volume  of  saturated  steam  under  atmospheric 
pressure  and  at  boiling-point  is  26.60  cubic  feet  or  1.661  cubic 
metres.  Solving  equation  (166)  for  C, 

cp    k  —  I 

^-J'-^~'T-p\ 
(^  —  ___ 


P  * 

%» 

and  therefore  we  have — 
French  system, 

c^  51.28  X  373-7  -  IQ333  X  i .66 1 

10333* 

English  system, 


_  9346  X  672.7  —  2116.32  X  26.60  _ 

L  —      - 1  —  971. 

2116.32  _ 

Substituting  the    constants  in  the  characteristic  equation, 
gives — 

French  system,          pv  =  51. $T  —  igSft.     .     .     .     .     .     (183) 

English  system,        pv  —  93.5  T  —  97 1/* (l84)' 


122  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Zeuner's  constants  for  equation  (183)  differ  from  those  given, 
since  he  used  424  for  the  mechanical  equivalent  of  one  calorie, 
and  273  for  the  absolute  temperature  of  freezing-point,  in  this 
connection  and  in  calculating  his  tables  for  saturated  steam. 

In  using  these  equations  for  superheated  steam  it  is  to  be 
remembered  that  the  pressures  are  specific  pressures,  i.e.,  kilo- 
grams per  square  meter  or  pounds  per  square  foot,  whereas  the 
pressures  of  saturated  steam  are  commonly  stated  in  milli- 
meters of  mercury  or  in  pounds  on  the  square  inch. 

Specific  Heat  at  Constant  Volume.  —  The  specific  heat  of 
superheated  steam  at  constant  volume  may  be  calculated  by 
applying  equation  (164)  to  the  case  of  saturated  steam.  The 
following  table  gives  the  values  obtained  at  several  pressures  : 

SPECIFIC  HEAT  OF  SUPERHEATED   STEAM. 

Pressures,  pounds  )  5o  IOQ         2QQ 

per  square  inch,    ) 
Specific  heat,  c,  ,  0.351         0.348        .346        .344        .341 

This  table  develops  the  fact  already  mentioned,  that  the 
specific  heat  of  superheated  steam  at  constant  volume,  deduced 
from  the  form  of  the  characteristic  equation  (i  66)  -and  the 
known  properties  of  saturated  and  superheated  steam,  is  a 
variable.  This  conclusion  applies  properly  to  steam  that  is  only 
slightly  superheated,  whereas  our  experimental  knowledge  of 
the  properties  of  superheated  steam  relates  to  steam  that  is 
superheated  to  a  marked  degree.  It  is  quite  as  reasonable  to 
suppose  that  the  specific  heat  at  constant  volume  is  constant, 
as  to  suppose  that  the  specific  heat  at  constant  pressure  is  con- 
stant, as  has  been  assumed.  Had  the  specific  heat  at  constant 
volume  been  assumed  to  be  constant,  and  had  the  character- 
istic equation  been  assumed  to  have  the  form 


then  the  specific  heat  at  constant  pressure  would  have  appeared 
to  be  variable.     A  complete  set  of  equations  could  be  worked 


SUPERHEATED   STEAM.  123 

out  under  such  an  assumption  that  would  be  on  as  good  a  basis 
as  those  we  have  deduced.  The  form  that  has  been  deduced 
appears  to  be  more  useful  in  engineering  work  where  the  pres- 
sures are  more  commonly  given  than  the  volumes. 

Intrinsic  Energy.  —  The  combination  of  the  equation 


with  equation  (173)  gives 

dE  =  jl-j,  (vdp  +  pdv)  =  j^  d(pv). 


(185) 


In  this  equation  it  may  be  assumed  that  £0  is  the  increase 
of  intrinsic  energy  of  saturated  steam  at  atmospheric  pressure, 
above  that  of  water  at  freezing-point.  From  equation  (140), 

AE.  =  $0  +  p0; 

hence  the  increase  of  intrinsic  energy  of  superheated  steam, 
having  the  pressure  p  and  the  volume  v,  above  that  of  water  at 
freezing-point,  is 


Taking  the  values  of  q0  ,  p0,  p0,  and  VQ  from  the  tables  of  the 
properties  of  saturated  steam  at  boiling-point,  we  have  — 

French  system,         E  =  r—   -  pv  -\-  476.2;.     .    ".     .     .     (186) 

K  *—  ~   1 

English  system,        E  =  7—  -  pv  -\-  857.2  ...... 


Total  Heat.  —  By  total  heat  of  superheated  steam  is  meant 
the  heat  required  to  change  one  unit  of  weight  of  water  at 


124  THERMODYNAMICS  OF   THE   STEAM-ENGINE, 

freezing-point  into  superheated  steam  having  a  given  tempera- 
ture and  pressure.  It  may  be  divided  into  the  heat  equivalent 
of  the  intrinsic  energy  and  the  heat  equivalent  of  the  external 
work.  The  first  part  may  be  calculated  by  equation  (186)  or 
equation  (187).  The  second  part  maybe  assumed  to  be 

Apv. 

Using  the  same  character  that  has  been  used  for  the  total 
heat  of  saturated  steam, 

^ 
A  =  T up  +  Apv  -\-  const. ; 

K  —  I 

Ak 
.  * .    A  =  -r up  -j-  const. 

K          1 

Substituting  for  pv  from  equation  (166) 

X  =  CP(T  —  -jjp1^}  +  const,      .    -;    .     (188) 

or  replacing  the  constants  by  their  known  values,  we  have — 
French  system,     A,  =  0.4805  (T  —  3-86/1)  _[_  476.2  ;    .     .     (189) 
English  system,    A.  =  0.4805  (T—  1.038/1) +  857.2.  .     .     (190) 

Comparison  with  Experiments. — Experiments  on  the 
specific  volume  of  superheated  steam  were  made  by  Hirn,* 
from  the  report  of  which  Zeuner  selected  the  experimental  data 
in  the  following  table.  The  specific  volume  has  been  calculated 
by  aid  of  equation  (183),  and  placed  in  the  table  opposite  the 
experimental  results  to  show  the  comparison  of  the  character- 
istic equation  with  experiment. 

*Theorie  Mecanique  de  la  Chaleur. 


SUPERHEATED   STEAM. 
SPECIFIC    VOLUME    OF    SUPERHEATED    STEAM. 


125 


SPECIFIC  VOLUME. 

Cubic  meters. 

Pressure 

T 

in 
atmospheres. 

Centigrade. 

Hirn's 
experiments. 

Equation  (183). 

I 

118.5 

1.74 

1-75 

I 

141 

1.85 

1.87 

3 

200 

0.697 

0.699 

4 

165 

0.4822 

0.476 

4 

2OO 

0-522 

0.520 

4 

246 

0.5752 

0.577 

5 

162.5 

0.3758 

0.376 

5 

205 

0.414 

0.418 

The  following  table  shows  that  the  characteristic  equation 
for  superheated  steam  applies  fairly  well  to  the  limiting  case  of 
saturated  steam.  The  values  in  columns  2  and  4  were  taken 
directly  from  the  tables  of  the  properties  of  saturated  steam, 
and  those  in  column  6  were  calculated  in  the  usual  manner  for 
saturated  steam  with  x  =  I.  The  specific  volumes  in  column 
3  were  calculated  by  aid  of  the  empirical  equation  for  the  tem- 
peratures and  pressures  taken  from  tables  for  saturated  steam. 
Columns  5  and  7  were  calculated  by  equations  (184)  and  (178). 
The  latter  equation  gives  a  negative  change  of  entropy  for 
saturated  steam  for  increasing  pressure,  which  is  to  be  taken 
from  the  entropy  of  steam  at  freezing-point. 

APPLICATION  OF  EQUATION  (184)  TO  SATURATED  STEAM. 


Absolute 
pressure, 

SPECIFIC  VOLUMES. 
Cubic  feet. 

TOTAL  HEAT. 

ENTROPY. 

pounds 

per 

square 
inch. 

Tabular 

value. 

Equation 
(184)- 

Tabular 
value. 

Equation  ' 
(190) 

Equation 
(M5). 

Equation 
(178). 

I 

2 

3 

4 

5 

6 

7 

14.7 

26.60 

26.6 

1146.6 

1146.6 

.7484 

1-752 

30 

13-59 

13-7 

"58.3 

1158-4 

.6891 

.704 

60 

7.096 

7.12 

1171.2 

1171.0 

.6340 

-64I 

100 

4.403 

4.38 

1181.9 

1180.3 

•5945 

-598 

150 

3.0II 

3-00 

1191.2 

1190.2 

•5649 

.568 

2OO 

2.294 

2.30 

1198.4 

1198.5 

.5446 

•546 

300 

1-554 

1-57 

1209.3 

1207.2 

.5262 

•517 

126  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Adiabatic    Line. — Since    the    entropy   remains    constant 
during  an  adiabatic  change,  equation  (178)  gives 


/ 


This  equation  has  of  course  the  same  form  as  the  corre- 
sponding one  for  a  gas,  with  the  essential  difference  that  k  is 
an  arbitrary  constant,  while  K  is  the  ratio  of  the  specific  heats. 
Equations  may  also  be  deduced  in  terms  of  /  and  z/,  or  T  and 
v,  i.e., 

vkp  —  v*p0      =  const.,      ....     (192) 


V*-'  =  7>*-'  =  const  ......     (193) 

During  an  adiabatic  expansion,  in  which  external  work  is 
done  at  the  expense  of  the  intrinsic  energy,  the  degree  of  super- 
heating is  reduced,  and  if  the  expansion  be  carried  far  enough 
the  vapor  becomes  saturated,  and  then  moist.  In  such  case 
the  equation 

' 


or 

•£-  +  «,+  0.4805  log,  ^-  =  ^-+6,     .    .     (I94) 
-*  1  •*  I          2  1 

isv  taken. 

For  example,  let  the  initial  pressure  be  100  pounds  absolute 
per  square  inch,  and  the  initial  temperature  be  400°  F.  ;  re- 
quired the  condition  of  the  steam  after  an  adiabatic  expansion 
to  15  pounds  absolute.  Here  we  have 

*,  =  327°.6,         r,  =  884.0,         6,  =  0.4733, 
/,=  2i3°.o,         rf  =  965.1,         0a  =  0.3143; 

884.0  ,  860.7      965.1*. 

•  •  •  jnj  +  0.4733  +  0.4805  log.  ^g-  =  -^--  +  0.3  143  ; 
.-.  *  =  0.923. 


SUPERHEATED   STEAM.  12? 

Isodynamic  or  Isoenergic  Line.  —  The  equation  to  this 
line  is  obtained  from  equation  (185)  by  making  E  equal  to  £0  , 
so  that 

pv=pj>i~  const  ......     .     (195) 

The  isodynamic  line  for  superheated  steam,  like  that  for  a 
gas,  is  a  rectangular  hyperbola. 

The  combination  of  equation  (195)  with  the  characteristic 
equation  gives 


from  which  it  is  evident  that  the  isodynamic  line  for  super- 
heated steam  differs  from  the  isothermal. 

The  external  work  during  an  isodynamic  change  is 

=p1v,\oze^.      .     (196) 

Since  all  the  heat  applied  is  expended  in  external  work, 

Q  =  AW.     .......     (197) 

Isothermal  Line.  —  The  equation  to  the  isothermal  line  is 
obtained  from  the  characteristic  equation  by  making  T  con- 
stant, so  that 

pv=PJ>i-C(p*-p?)  .....     (198) 

The  heat  applied  during  an  isothermal  change  is  obtained 
by  integrating  equation  (172)  with  ^constant  ; 


.......    (199) 


We  have  also 


I3O  THERMODYNAMICS  OF   THE  STEAM-ENGINE. 

If  the  intrinsic  energy  of  a  unit  of  weight  of  the  fluid  in 
A  is  Elt  and  of  that  in  B  is  £3,  the  energy  changed  into  me- 
chanical work  is 

F  —  F 

J-'\         -^a* 

to  which  is  to  be  added  the  mechanical  equivalent  of  the  heat 
applied,  or 

Q 

A' 

Now  the  gain  of  kinetic  energy  of  motion,  if  the  velocity 
changes  from  wl  in  A  to  w^  in  B,  will  be,  for  each  unit  of  weight 
of  fluid, 


Assuming  that  all  of  the  work  applied  produces  change  of 
velocity  only, 

*£-i£=%+E>-E'+*>v>-*>v-  •  •  (20I> 

Incompressible  Fluids.  —  The  change  of  volume  of  most 
liquids  under  pressure  is  so  small  that  it  may  be  neglected,  in 
which  case  the  change  of  temperature  may  also  be  neglected 
and  the  intrinsic  energy  may  be  assumed  to  be  constant. 

Making  Q  =  o,  the  equation  (201)  reduces  to 

g-f  =(/,-/>„       .......      (202) 

since  vl  —  v^.     If  the  velocity  in  A  is  small  compared  with  that 
in  B,  we  may  suppress  the  subscript  and  write 

L=(A—  AK»  .......  (2°3) 


FLOW  OF  FLUIDS.  131 

which  is  the  usual  equation  given  in  hydraulics.  If  the  differ- 
ence of  pressure  is  due  to  a  difference  of  level,  or  head,  h,  we 
have 

A  —  A  =  hy, 

in  which  y  is  the  density,  equal  to-,  so  that 


(2°4) 


Flow  of  Gases.  —  The  most  important  case  for  gases  is 
flow  without  transmission  of  heat  —  that  is,  an  adiabatic  flow  ; 
in  which  case  Q  becomes  zero.  Equation  (84)  gives 


so  that  equation  (201)  reduces  to 


(205) 


Usually  the  initial  velocity  is  zero,  in  which  case  the  sub- 
script may  be  dropped,  and  we  may  write 

W*  K 

—  =  (A*'i-A*'.)—  —  ......    (206) 

For  an  adiabatic  transformation 


130  THERMODYNAMICS  OF   THE  STEAM-ENGINE. 

If  the  intrinsic  energy  of  a  unit  of  weight  of  the  fluid  in 
A  is  Elt  and  of  that  in  B  is  Et,  the  energy  changed  into  me- 
chanical work  is 

77       p 
**\      •***» 

to  which  is  to  be  added  the  mechanical  equivalent  of  the  heat 
applied,  or 

Q 

A 

Now  the  gain  of  kinetic  energy  of  motion,  if  the  velocity 
changes  from  wt  in  A  to  z£/2  in  B,  will  be,  for  each  unit  of  weight 
of  fluid, 


Assuming  that  all  of  the  work  applied  produces  change  of 
velocity  only, 


Incompressible  Fluids.  —  The  change  of  volume  of  most 
liquids  under  pressure  is  so  small  that  it  may  be  neglected,  in 
which  case  the  change  of  temperature  may  also  be  neglected 
and  the  intrinsic  energy  may  be  assumed  to  be  constant. 

Making  Q  =  o,  the  equation  (201)  reduces  to 


(202) 


since  vl  =  v^.     If  the  velocity  in  A  is  small  compared  with  that 
in  B,  we  may  suppress  the  subscript  and  write 


vr       ,            .  , 

--(A -AX, (203) 


FLOW  OF  FLUIDS.  131 

which  is  the  usual  equation  given  in  hydraulics.  If  the  differ- 
ence of  pressure  is  due  to  a  difference  of  level,  or  head,  h,  we 
have 


in  which  y  is  the  density,  equal  to  —  ,  so  that 


(204) 


Flow  of  Gases.  —  The  most  important  case  for  gases  is 
flow  without  transmission  of  heat  —  that  is,  an  adiabatic  flow  ; 
in  which  case  Q  becomes  zero.  Equation  (84)  gives 

p-     $v 

~  K-l> 

so  that  equation  (201)  reduces  to 


*         W* 


(205) 


Usually  the  initial  velocity  is  zero,  in  which  case  the  sub- 
script may  be  dropped,  and  we  may  write 


tt  (2o6) 


For  an  adiabatic  transformation 


-zsi-  '    '  (207) 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


The  characteristic  equation  for  gases,  and  the  application 
to  it  of  the  first  law  of  thermodynamics,  give  the  two  equations 


'*  —  <-v 


A   ' 


••J-2E-&P] 


(208) 


Again, 


so  that 


(209) 


If  the  area  of  the  orifice  is  F,  then  the  weight  of  air  dis- 
charged per  second  is 

Fw  , 

Lr  =  --  > 

^2 

or,  substituting  for  w  its  value  from  equation  (207), 


=  ^  I  ?^wf 

(   /c-i 


or,  substituting  for  v*  its  value 


/ 


.      .      (210) 


Now  G  will  be  a  maximum  when 


FLO  W  OF  FLUIDS.  133 


is  a  maximum.     Differentiating  and  equating  the  first  differen 
tial  coefficient  to  zero  gives  after  reduction 


A 

Putting  for  /r  its  value  1.405,  gives  for  the  ratio  of  pressures 
producing  the  maximum  flow 


The  equations  deduced  for  the  flow  of  gases  can  properly 
be  applied  only  to  the  flow  from  one  tube  into  another  of 
smaller  diameter  when  the  specific  pressure  (or,  as  a  substitute 
therefor,  the  specific  volume,  or  the  temperature)  in  the  smaller 
tube  is  known,  as  well  as  the  initial  condition  in  the  large  tube. 
In  making  experiments  on  the  flow  of  gases  and  vapors,  it  has 
been  customary  to  allow  the  fluid  in  the  tube  to  discharge  into 
the  atmosphere  or  into  a  reservoir,  and  to  assume  that  the  pres- 
sure in  the  tube  is  the  same  as  that  in  the  reservoir  :  and  when 
the  lower  pressure  is  less  than  half  the  upper  pressure  such  ex- 
periments with  that  assumption  show  an  actual  flow  greater 
than  the  calculated  flow  and  often  very  much  greater. 

It  was  first  suggested  by  Mr.  R.  D.  Napier,  in  connection 
with  experiments  made  by  him  on  the  flow  of  steam,  that  the 
pressure  in  the  small  tube  is  not  necessarily  the  pressure  of 
the  atmosphere  or  of  the  reservoir  into  which  it  delivers  ;  he 
further  suggested  that  the  pressure  in  the  tube  is  never  less 
than  that  pressure  which  gives  a  maximum  flow. 

Professor  Fliegner  *  found  that  the  pressure  in  the  throat 
of  a  well-rounded  orifice  through  which  air  is  flowing  is  never 
less  than  0.57  of  the  absolute  pressure  in  the  reservoir  from 
which  the  flow  takes  place.  The  mean  of  a  large  number  of 

*  Der  Civilingenieur,  vol.  xx.  p.  14.     1874. 


134  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

experiments  with  two  well-rounded  orifices,  4.085  and  7.314 
mm.  in  diameter  at  the  throat,  showed  that  when  the  pressure 
in  the  reservoir  was  more  than  double  the  pressure  of  the  air, 
the  pressure  in  the  throat  was  0.5767  of  the  pressure  in  the 
reservoir.  The  pressure  in  the  reservoir  varied  from  3366  mm, 
of  mercury  to  808  mm.  The  number  0.5767  is  very  nearly  equal 

i 
to  ~7r  ,  and  is  to  be  compared  with  the  ratio  for  maximum  flow 

given  above.  In  equation  (210)  substitute  for  vl  its  value  from 
the  equation 

AV,  =*  47;, 

and  we  have 


in  which  K  =  1.405  and  —  =  0.5767  ; 

A 


For  the  flow  into  the  atmosphere  from  a  reservoir  having  a 
pressure  less  than  twice  the  atmospheric  pressure,  Fliegner 
found  the  empirical  equation 


=  0.5622 


These  equations  were  found  to  be  justified  by  a  comparison 
with  experiments  on  the  flow  of  air,  made  by  Fliegner  himself, 
by  Zeuner  and  by  Weisbach. 

Although  these  equations  were  deduced  from  experiments 
made  on  the  flow  of  air  into  the  atmosphere,  it  is  probable  that 
they  may  be  used  for  the  flow  of  air  from  one  reservoir  into 
another  reservoir  having  a  pressure  differing  from  the  pressure 
of  the  atmosphere. 


FLOW  OF  FLUIDS.  135 

Fliegner's  Equations  for  Flow  of  Air.—  Introducing  the 
values  for  g  and  R  in  the  equations  deduced  by  Fliegner,  we 
have  the  following  equations  for  the  French  and  English  sys- 
tems of  units: 


fl>2fa 


French  Units. 


English  Units. 

A 
£  =  0.530  F-^=r, 


=  1. 060  F 


pl  =  pressure  in  reservoir ; 
pa  =  pressure  of  atmosphere  ; 

Tl  =  absolute  temperature  of  air  in  reservoir;  degrees  centi- 
grade, French  units ;  degrees  Fahrenheit,  English  units. 

In  the  English  system  pl  and  pa  are  pounds  per  square  inch, 
and  F  is  the  area  of  the  orifice  in  square  inches,  while  G  is  the 
flow  of  air  through  the  orifice  in  pounds  per  second.  If  desired, 
the  area  may  be  given  in  square  feet  and  the  pressures  in  pounds 
on  the  square  foot,  as  is  the  common  convention  in  thermo- 
dynamics. 

In  the  French  system  G  is  the  flow  in  kilograms  per  second. 
The  pressures  may  be  given  in  kilograms  per  square  meter  and 
the  area  F  in  square  meters  ;  or  the  area  may  be  given  in  square 
decimeters  or  square  centimeters,  and  the  pressures  in  kilograms 
on  the  same  unit  of  area  used  in  connection  therewith.  If  the 
pressures  are  in  millimeters  of  mercury,  multiply  by  13.5959;  if 
in  atmospheres,  multiply  by  10333. 


136  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Maximum  Velocity  of  Flow.  —  According  to  the  kinetic 
theory  of  gases,  the  pressure  of  a  gas  on  the  walls  of  the  con- 
taining vessel  is  due  to  the  impact  of  the  molecules  of  the  gas. 
To  estimate  the  mean  velocity  of  the  molecules  Joule  *  pro- 
ceeds in  the  following  manner  :  The  weight  of  one  cubic  meter 

of  gas  is  -  ,  and  the  pressure  which  it  exerts  on  each  of  the  six 
sides  of  a  cubical  vessel  containing  it  is  /.  Suppose  that  the 
weight  —  of  the  gas  to  be  divided  into  three  equal  portions,  one 

of  which  oscillates  between  each  pair  of  faces  of  the  cube  and 
produces  the  pressure  by  impact,  first  on  one  and  then  on  the 
other  of  the  pair.  Now,  if  a  body  have  a  velocity  equal  to^*,  it 
will  be  brought  to  rest  by  a  force  equal  to  its  weight  acting  on 
it  for  one  second  ;  and  that  force  acting  for  two  seconds  will 
bring  it  to  rest  and  then  impart  to  it  the  same  velocity  in  the 
opposite  direction.  In  two  seconds  there  will  be  g  impacts  on 
each  of  the  pair  of  faces,  and  it  will  be  assumed  that  the  effect 

of  the  impacts  is  equal  to  that  of  a  pressure  equal  to  -  -  kilo- 

grams on  each  face  ;  that  is,  on  one  square  meter.  The  pres- 
sure will  vary  as  the  square  of  the  velocity,  since  both  the  force 
required  to  reverse  the  velocity  and  the  number  of  impacts  in- 
crease with  the  velocity.  Finally,  Joule  makes 

u*  =  p  -.  ---  . 
3^ 

in  which  u  is  the  mean  velocity  of  the  molecules  of  the  gas. 
This  may  be  written 


Fliegner  assumes  that  the  maximum  velocity  with  which  a 
gas  can  flow  through  an  orifice  is 

«W  =  V^RT,  =  16.9  1/7; 
when  the  French  system  of  units  is  used. 

*  Memoir  Phil.  Soc.,  vol.  ix.  p.  107. 


FLOW  OF  FLUIDS.  137 

But  if  we  make  ~  =  0.5767  in  equation  (207),  the  velocity 
becomes,  for  French  units, 

•7ft  17    I 

^max.  / 

Weisbach's  Experiments  on  the  Flow  of  Air. — Weis- 
bach  *  gives  for  the  velocity  of  air  through  an  orifice  into  the 
atmosphere 


and  by  its  use  he  finds  for  the  coefficient  of  flow,  from  his  own 
experiments,  the  results  given  in  the  following  tables : 

FLOW   OF  AIR  THROUGH  AN   ORIFICE. 
Diameter  I  centimeter. 

Ratio  of  pressures-       1.05       1.09       1.43      1.65       1.89      2.15 

Coefficient  0.555     0.589    0.692    0.724    0.754    0.788 

Diameter  2.14  centimeters. 

Ratio  of  pressures—      1.05          1.09          1.36         1.67         2.01 
Coefficient  0.558       0.573       0.634       0.678       0.723 

FLOW  OF  AIR  THROUGH   A  SHORT  TUBE. 
Diameter  I  centimeter,  length  3  centimeters. 

Ratio  of  pressures  —  1.05  i.io  1.30 

Coefficient  0.730  0.771  0.830 

Diameter  1.414  centimeters,  length  4.242  centimeters. 

Ratio  of  pressures  ^  1.41  1.69 

Coefficient  0.813  0.822 

*  Mechanics  of  Engineering. 


138  THERMODYNAMICS  OF  THE   STEAM-ENGINE. 

Diameter  I  centimeter,  length  1.6  centimeters,  orifice  rounded. 

Ratio  of  pressures  ^—      1.24         1.38         1.59         1.85         2.14 
Coefficient  0.979      0.986      0.965       0.971       0.978 

Flow  of  Saturated  Vapor.  —  For  a  mixture  of  a  liquid  and 
its  vapor  equation  (140)  gives 


so  that  equation  (201)  gives  for  the  adiabatic  flow  from  a  re- 
ceptacle in  which  the  initial  velocity  is  zero, 

—  =  ~2  &  ~  &  +  *J*  -  *>#>)  +  A^i  -  /,*'•  •    •    (211) 
Substituting  for  vt  and  v^  from 

V  =  XU  -\-  <T, 

w* 


^  +  Acr(j>l  ~/3). 


But 


-A).  •    (212) 


The  last  term  of  the  right-hand  member  is  small,  and  fre- 
quently can  be  omitted. 

The  value  of  x^  in  the  tube  B,  Fig.  29,  at  a  distance  from 
the  orifice,  can  be  determined  by  the  equation 


= 
*  i 


FLOW  OF  FLUIDS.  139 

or,  if  the  proper  tables  are  lacking,  we  may  use  the  approxi- 
mate form, 


It  is  necessary  to  remember  that  while  the  tables  commonly 
give  the  pressure  in  pounds  on  the  square  inch,  or  in  atmos- 
pheres, etc.,  /,  and  /a  in  the  last  term  of  equation  (212)  are  the 
specific  pressures  ;  that  is,  the  pressures  in  pounds  on  the  square 
foot,  or  kilograms,  on  the  square  meter. 

Substituting  the  first  form  for  x^,  equation  (212)  gives 


Substituting  the  second  form  in  equation  (212),  and  neglect- 
ing the  last  term,  we  have  the  approximate  formula 


(214) 


The  weight  of  fluid  that  will  pass  through  an  orifice  having 
an  area  of  F  square  meters  or  square  feet  may  be  calculated 
by  the  formula 


The  equations  deduced  are  applicable  to  all  possible  mix- 
tures of  liquid  and  vapor,  including  dry  saturated  steam  and 
pure  hot  water.  In  the  first  place  steam  will  be  condensed  in 
the  tube,  and  in  the  second  water  will  be  evaporated. 

If  steam  blows  out  of  an  orifice  into  the  air,  or  into  a  large 
receptacle,  and  comes  to  rest,  the  energy  of  motion  will  be 
turned  into  'heat  and  will  superheat  the.  steam.  Steam  blow- 
ing into  the  air  will  be  wet  near  the  orifice,  superheated  at  a 
little  distance,  and  if  the  air  is  cool,  will  show  as  a  cloud  of 
mist,  further  from  the  orifice. 


140  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Napier's  Formulae  for  Flow  of  Steam.—  As  the  result 
of  a  large  number  of  experiments  made  on  the  flow  of  steam 
Mr.  R.  D.  Napier  concludes  that  the  pressure  in  the  throat  of 
an  orifice  from  which  steam  is  flowing  is  never  less  than  that 
pressure  which,  compared  with  the  pressure  in  the  reservoir, 
will  give  the  maximum  flow. 

The  following  approximate  equations  may  be  used  with  the 
English  system  of  units  : 


in  which  pl  is  the  pressure  in  the  reservoir,  and  pa  is  the  pres- 
sure of  the  atmosphere,  in  pounds  on  the  square  inch,  and  G  is 
the  flow  in  pounds  per  second  through  an  orifice  having  an  area 
of  F  square  inches. 

Rankine*  concludes,  from  an  examination  of  Napier's  ex- 
periments and  a  comparison  of  them  with  formulae  proposed 
by  him,  and  a  comparison  of  both  with  thermodynamic  .For- 
mulas, that  the  principle  that  the  pressure  in  an  orifice  is  never 
less  than  that  which  gives  the  maximum  flow  is  well  substan- 
tiated, and  that  the  above  equations  may  be  used  for  rough 
calculations. 

Experiments  on  Flow  of  Steam.  —  The  theory  of  the 
adiabatic  flow  of  steam  should  apply  to  all  mixtures  of  water 
and  steam,  including  clear  water,  as  from  the  water  space  of  a 
boiler.  Zeunerf  points  out  an  opportunity  thus  afforded  of 
testing  the  equations,  but  states  that  experiments  made  by 
blowing  water  out  of  a  locomotive  boiler  gave  unsatisfactory 
results. 

Some  experiments  were  made  by  Mr.  B.  G.  Buttolph  $  in 
the  laboratories  of  the  Institute  of  Technology  on  the  flow  of^ 
steam  through  a  brass  tube  0.275  of  an  inch  in  internal  diame-  c 

*  The  Engineer,  vol.  xxvii.  p.  359.     1869. 

\  Mechanische  Warmetheorie. 

\  Proceedings  Am.  Mech.  Eng.  Soc.  1888. 


FLOW  OF  FLUIDS. 


ter  and  eight  inches  long,  and  having  the  entrance  orifice 
rounded  to  reduce  contraction.  The  results  are  given  in  the 
following  table : 

FLOW   OF   SATURATED   STEAM. 


Num- 
ber 
of 

GAUGE  PRESSURES. 
Pounds  per  square 
inch. 

Differ- 
ence of 

Pressure  of 
Atmosphere 
by  Barome- 

Flow in 
Pounds 

Experi- 
ment. 

At  En- 

At Exit. 

Pressures. 

ter. 
Pounds. 

per  Hour. 

trance. 

I 

69.1 

4.4 

64.7 

14.7 

229.0 

2 

69.6 

9-7 

59-9 

14.7 

230.4 

3 

71-3 

14.8 

56.6 

14.7 

242.0 

4 

69.I 

19.4 

49-7 

232.0 

5 

71.0 

24.4 

46.5 

.... 

234-5 

6 

70-3 

29.1 

41.2 

.... 

229.0 

7 

72.0 

34-2 

37-8 

14.8 

232.0 

8 

72.O 

39-5 

32.5 

I4.8 

221  .4 

9 

71.6 

44-2 

27.4 

14.7 

216.5 

The  following  table  gives  the  results  of  some  experiments 
on  the  flow  of  steam  through  an  orifice  0.25  of  an  inch  in  diam- 
eter, in  a  thin  plate,  made  by  Mr.  G.  P.  Aborn  *  in  the  labora- 
tories of  the  Institute. 

FLOW   OF   STEAM   THROUGH   AN   ORIFICE. 


Number  of 
Experiment. 

Higher 
Pressure. 

Difference  of 
Pressure. 

Flow  in  Pounds 
per  Hour  by  Tank. 

I 

71.8 

0.92 

29.7 

2 

71-5 

1.85 

43-1 

3 

71-9 

2.79 

52.6 

4 

71.6 

3.89 

67.6 

5 

71.9 

5-55 

77-6 

6 

7i.8 

6.50 

84.2 

7 

71.7 

8.07 

91.8 

8 

72-9 

9-23 

93-9 

9 

72.5 

12.8 

110.3 

10 

73-7 

15-9 

124.9 

ii 

72.7 

21.  1 

I4L5 

12 

74-2 

27.O 

156.8 

13 

71.9 

33-7 

166.3 

14 

74-3 

41.0 

180.7 

15 

72.7 

49-2 

187.7 

16 

72.9 

57.0 

195.8 

17 

73.7 

64.4 

196.9 

18 

72.0 

68.4 

197.8 

*  Thesis,  1886. 


142  THERMODYNAMICS  OF  THE   STEAM-ENGINE. 

Flow  of  Superheated  Steam. — Equation  (185)  gives  for 
the  change  of  intrinsic  energy 


so  that  for  an  adiabatic  flow 

w*  k 

^=(M~M);g—  ,   ......    (216) 

which,  by  aid  of  equation  (194),  may  be  reduced  to 
w*  k 


Equations  (216)  and  (217)  have  the  same  form  as  the  corre- 
sponding equations  for  a  gas,  since  the  expression  for  intrinsic 
energy  has  the  same  form  for  superheated  steam  as  for  a  gas. 

Substituting  for  /^  from  the  characteristic  equation, 


-(f)}     •     '     •     (-8) 

For  calculation  either  equation  (217)  or  (218)  can  be  used, 
as  may  be  convenient. 

EXAMPLES. 

1.  Find  the  velocity  of  flow  of  air  from  the  pressure  of  6 
atmospheres  in  a  reservoir  to  the  pressure  of  5  atmospheres  in 
the  throat  of  the  orifice ;  also,  from  5  to  4  atmospheres,  from 
4  to  3,  and  from  3  to  2,  the  initial  temperature  in  each  case 
being  30°  C. 

2.  Find  the  weight  of  air  per  second  that  will  be  discharged 
from  an  orifice  I  inch  in  diameter,  from  a  reservoir  having  the 
temperature  60°  F.  and  a  pressure  of  150  pounds  per  square 
inch,  into  the  atmosphere.     Calculate  also  with  initial  pressures 
100,  50,  30,  and  20  pounds  absolute. 

3.  Find  the  weight  of  saturated  steam  per  second,  discharged 
through  an  orifice  I  inch  in  diameter,  from  a  boiler  having  the 


FLOW  OF  FLUIDS.  143 

gauge  pressure  60  pounds,  into  the  atmosphere.  Find  also  for 
the  following  values  of  x,  90,  80,  60,  50,  40,  20,  and  for  hot 
water.  Calculate  also  for  initial  pressures  80,  100,  150,  300 
pounds  by  the  gauge. 

4.  Find  the  velocity  of  flow  of  superheated  steam  with  the 
initial  temperature  600°  F.  and  initial  pressure  30  pounds  by 
the  gauge,  when  the  pressure  in  the  throat  of  the  orifice  is  20 
pounds  by  the  gauge. 

5.  In   Example  4  find  the  weight  per  second  discharged 
through  an  orifice  I  inch  in  diameter. 


CHAPTER   X. 

INJECTORS. 

AN  injector  is  an  instrument  by  means  of  which  a  jet  of 
steam  acting  on  a  stream  of  water  with  which  it  mingles,  and 
by  which  it  is  condensed,  can  impart  to  the  resultant  jet  of 
water  a  sufficient  velocity  to  overcome  a  pressure  that  may  be 
equal  to  or  greater  than  the  initial  pressure  of  the  steam. 
Thus,  steam  from  a  boiler  may  force  feed-water  into  the  same 
boiler,  or  into  a  boiler  having  a  higher  pressure.  The  mechani- 
cal energy  of  the  jet  of  water  is  derived  from  the  heat  energy 
yielded  by  the  condensation  of  the  steam-jet.  Similar  instru- 
ments are  used  in  which  a  jet  of  stearn  or  air  imparts  motion 
to  a  stream  of  air,  or  a  jet  of  water  imparts  motion  to  a  stream 
of  water,  without  a  change  of  heat  into  mechanical  energy. 

When  the  reservoir  from  which  water  is  drawn  is  below 
the  injector,  the  injector  is  called  a  lifting  injector ;  but  when 
the  reservoir  is  above  the  injector,  so  that  water  will  flow  in 
under  the  action  of  gravity,  it  is  called  a  non-lifting  injector. 


10 

FIG.  30. 

Fig.  30  shows  the  section  of  the  Mack  lifting  injector,  and  Fig. 
31  of  the  non-lifting  injector,  by  the  same  maker. 

Method  of  Working. — To  start  the  lifting  injector,  open 
the  steam-valve  a  quarter  or  half  of  a  turn,  then  open  the  valve 

144 


INJECTORS. 


145 


in  the  water  supply ;  as  soon  as  water  appears  at  the  overflow 
open  the  steam-valve  until  it  ceases  to  overflow. 

When  the  steam-valve  is  first  opened  a  part  of  a  turn  the 
hollow  spindle  5  is  farther  to  the  left  and  closes  the  orifice  6. 
A  small  stream  of  steam  flows  past  5,  passes  through  the  con- 
ical passage,  and  out  at  the  overflow.  The  stream  of  steam 
flowing  past  6  draws  air  with  it  from  the  chamber  5,  and  the 
partial  vacuum  thus  produced  draws  water  from  the  reservoir, 
which  condenses  the  steam,  and  with  it  flows  out  at  the  over- 


flow in  a  continuous  stream.  When  this  stream  is  well  estab- 
lished the  steam-valve  is  opened  wide,  and  a  large  jet  flows  past 
6,  and  is  condensed  in  contact  with  the  stream  of  water.  The 
stream  of  water  flowing  through  the  comical  passage  has  now 
sufficient  velocity  to  leap  across  the  opening  at  o  and  enter  the 
conical  passage  7,  from  whence  it  passes  to  the  boiler.  At  the 
overflow  is  a  valve,  held  open  by  a  slender  spring,  which  closes 
when  the  pressure  at  o  is  less  than  that  of  the  atmosphere,  so 
that  air  may  not  be  forced  into  the  boiler  with  the  feed-water. 

It  is  customary  to  have  a  valve  in  the  steam-pipe  above  the 
injector,  which  is  closed  when  the  injector  is  not  working,  and 
which  is  opened  before  starting  the  injector.  It  is  necessary 
to  have  a  check-valve  in  the  boiler  feed-pipe  to  prevent  the 
water  in  the  boiler  from  flowing  back  through  the  injector 
when  the  injector  is  not  working. 

The  action  of  the  injector  may  be  regulated,  within  limits,* 


146  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

by  manipulating  the  water-  or  steam-valve,  or  both.  When  the 
pressure  of  the  steam  is  low  or  the  lift  small,  it  may  be  neces- 
sary to  reduce  the  flow  of  water  by  partially  closing  the  water- 
valve. 

To  start  the  non-lifting  injector  the  steam- valve  is  opened 
to  clear  the  supply-pipe  of  condensed  water,  and  then  it  is 
closed.  The  water-valve  is  opened  till  water  appears  at  the 
overflow,  upon  which  the  steam-valve  is  opened  till  water 
ceases  to  run  out  at  the  overflow. 

It  is  apparent  that  the  action  and  the  construction  of  this 
form  are  simpler  than  those  of  the  lifting  injector. 

Theory  of  the  Injector.— The  efficiency  of  an  injector 
and  the  proper  proportion  of  its  parts  cannot  be  determined 
entirely  from  the  known  properties  of  steam,  the  more  espe- 
cially as  its  action  depends  on  the  flow  of  steam.  We  shall 
first  study  its  action  under  the  assumptions  that  there  is  no 
loss  from  friction  and  radiation,  and  that  we  may  use  the  equa- 
tions for  the  adiabatic  flow  of  steam.  It  will  also  be  assumed 
that  the  jet  of  steam  at  6,  Fig.  30,  is  immediately  and  com- 
pletely condensed  by  contact  with  the  stream  of  water  there. 

The  quantities  to  be  ascertained  are : 

1.  The  velocity  with  which  the  steam  issues  from  6,  Fig. 
30.     This  depends  on  the  pressure  and  quality  of  the  steam  in 
the  supply-pipe,  and  the  pressure  of  the  orifice  6. 

2.  The  quantity  of  feed-water  that  one  pound  of  steam  will 
force  into  the  boiler.     This  depends  on  the  temperature  of  the 
water  in  the  reservoir,  the  temperatures  of  the  water  in  the  feed- 
pipe, and  the  pressure  of  the  steam  in  the  boiler  from  which 
steam  is  drawn  and  to  which  water  is  fed. 

3.  The  velocity  with  which  the  stream  of  water  passes  the 
narrowest  orifice  at  7  on  the  way  to  the  boiler. 

4.  The  size  of  the  steam  and  water  orifices. 

Velocity  of  the  Steam-jet. — Assuming  that  the  flow  of 
steam  from  the  orifice  6  is  adiabatic,  equation  (212)  gives 


O 


INJECTORS.  147 

in  which  pl  is  the  pressure  of  the  steam  in  the  supply-pipe,  and 
/„  the  pressure  in  the  orifice  6.  x^  ,  rlt  and  ql  are  the  quality  of 
the  steam,  the  heat  of  vaporization,  and  the  heat  of  the  liquid 
of  the  steam  at  the  pressure  p^  ;  and  ;ra,  rt,  and  q^  are  the  cor- 
responding properties  at  the  pressure  /a. 
To  determine  x^  we  have 

**r*  _J_  0  —  Xtf*  JL.  e 

^        —'  V* 


Quantity  of  Feed-water  per   Pound  of  Steam.  —  The 

number  of  pounds  of  feed-water  y  delivered  by  one  pound  of 
steam  may  be  found  by  assuming  only  that  the  losses  from  fric- 
tion and  radiation  may  be  neglected. 

The  gain  of  heat  by  the  feed-water  in  passing  from  the  tem- 
perature /3  in  the'  reservoir  to  the  temperature  /4  in  the  feed- 
pipe is 

' 


The  loss  of  heat  in  one  pound  of  s^feeam  on  condensation 
and  reduction  to  the  temperature  /4  is 


The  heat  equivalent  of  the  kinetic  energy  of  the  jet  of  water 
at  its  smallest  section,  where  the  velocity  is  V,  which  energy  is 
expended  in  forcing  the  water  into  the  boiler,  is 

A  V 


The  assumption  of  no  loss  of  heat  gives 

A  V 

=  *^ 


(219) 


An  approximate  value  of  y  can  be  obtained  by  neglecting 
the  term  containing  V,  so  that 


148  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

An  exact  value  of  y,  in  the  general  case,  can  be  obtained 
by  a  series  of  approximations  in  combination  with  equation 
(222),  the  first  approximation  being  obtained  by  aid  of  equa- 
tion (220). 

Velocity  of  the  Water-jet.—  Three  cases  may  occur  in 
different  forms  of  injectors  : 

1.  The  water  in  the  supply-pipe  may  have  a  head  S,  and 
the  approaching  water  will  have  a  momentum  imparted  to  it 
by  that  head. 

2.  The  water  in  the  supply-pipe  may  be  lifted  through  a 
height  5,  and  a  corresponding  momentum  must  be  imparted 
to  it  by  the  steam-jet. 

3.  There  may  be  neither  lift  nor  head,  and  the  approaching 
water  will  have  no  momentum. 

The  first  may  be  considered  to  be  the  gerieral  case,  and  may 
be  made  to  include  the  other  two  by  making  the  head  nega- 
tive for  one  and  zero  for  the  other. 

The  momentum  of  I  -(-  y  pounds  of  water,  at  the  smallest 
section  of  the  water-jet,  will  be  the  sum  of  the  momentum  of 
one  pound  of  moist  steam  in  the  steam-jet,  plus  the  momentum 
imparted  to  I  -\-  y  pounds  of  feed-water  by  the  head  5. 

The  momentum  of  i  -f-  y  pounds  of  water  in  the  water-jet  is 


The  momentum  of  one  pound  of  steam  is 

w 
g 

Let  a  be  the  area  of  the  smallest  section  of  the  water-jet  ; 
ihen  the  force  exerted  by  the  head  of  S  water  having  the  den- 
sity y  on  that  area  is 

Syaw. 

This  force  acts  on  a  mass 


INJECTORS.  149 

of  water  per  second,  and  imparts  to  it  a  velocity  of 

Vyaw      Sg 


feet  per  second,  so  that  the  momentum  imparted  to   I  +  y 
pounds  of  water  by  the  head  5  is 

Sg. 


Hence  we  have 


IV 


•     -•;        .        (222) 


For  the  second  case,  in  which  the  water  is  lifted  by  the  in- 
jectors through  a  height  7z, 


v=4rr*  +  \/^-^-Sg>    •    •    (223) 


For  the  third  case,  in  which  the  water  enters  the  injector 
on  the  level  of  the  jets,  so  that  the  momentum  of  one  pound 
of  steam  in  the  steam-jet  imparts  the  momentum  which  I  -\~ y 
pounds  of  water  has  in  the  water-jet,  we  have 

(i  +  y]  V     w 


which  maybe  obtained  from  equation  (221)  by  making  5 zero. 


ISO  THERMODYNAMICS  OF  THE   STEAM-ENGINE. 

Sizes  of  the  Orifices.  —  Since  one  pound  of  steam  feeds  y 
pounds  of  water  to  the  boiler,  the  steam  required  per  second 
to  feed  G  pounds  of  water  will  be 


The  specific  volume  of  the  moist  steam  in  this  orifice  is  as- 
sumed to  be 


where  x^  is  determined  by  the  equation  for  the  adiabatic  change 
from  the  pressure  pl  in  the  boiler  to  the  pressure  /2  before  the 
orifice.  Consequently  the  area  of  the  steam-orifice  in  square 
feet  is 

Gfr».  +  g). 

yw 

The  steam  used  by  an  injector  is  returned  to  the  boiler  with 
the  feed-water,  so  that 


pounds  of  water  per  second  pass  through  the  water-orifice.     Its 
area  in  square  feet  should  therefore  be 


The  density  y  should  properly  be  the  weight  of  water  per 
cubic  foot,  at  the  temperature  in  the  feed-pipe,  but  the  ordi- 
nary density  62.4  can  be  used  instead. 

In  all  of  the  foregoing  work  the  English  units  have  been 
used,  but  the  equations  may  be  applied  to  problems  stated  in 
the  French  units,  kilograms,  and  meters,  without  change.  They 
may  also  be  applied  to  other  vapors  that  behave  like  steam. 

The  diameters  of  the  orifices  of  an  injector  are  commonly 
given  in  millimeters  or  inches  and  fractions,  while  the  areas  by 


INJECTORS.  151 

the  formulae  are  given  in  square  feet  or  square  meters.     The 
reductions  are  readily  made  in  every  case. 

PROBLEM. — Required  the  diameters  of  the  orifices  for  an 
injector  to  deliver  1200  gallons  of  water  per  hour  ;  the  tempera- 
ture of  the  feed-water  being  180°  F.,  and  that  of  the  water  in 
the  reservoir  100°  F.,  while  the  pressure  in  the  boiler  is  45 
pounds.  Assuming  the  steam  supplied  to  the  injector  to  be 
dry,  and  that  the  pressure  in  the  steam-orifice  is  0.6  of  the  ab- 
solute boiler  pressure,  we  have  for  the  determination  of  the 
quality  of  the  steam  in  the  steam-orifice 


/.  x  =  0.9683. 

The  last  term  of  equation  (212)  may  here  be  neglected,  so 
that 

Aw* 

—  =  909.5  -  902.1  +  261.6  -  229.7  =  39.3  ; 

•'•  w  =  4/2  X  32.2  X  39-3  X  778  =  1403. 
The  quantity  of  water  delivered  per  pound  of  steam  is 

_  9°9-5  +  261.6  —  148.5  _ 
148.5  -  68.0 

The  velocity  of  the  water-jet  is 

V  =  -  — —  =  102.4  ft.  per  sec. 
13.70 

The  injector  is  required  to  deliver  1200  gallons  an  hour,  or 

1200  X  231 
1728  X  60  X  60  =  ao4456  cubic  ft.  per  sec ; 

.-.  G  =  0.04456  X  62.4  =  2.781  pounds  per  sec. 


152  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  specific  volume  of  the  moist  steam  in  the  steam-orifice 
is 

x*u*  +  °"  —  0.9683  X  11.50  +  0.016  =  11.15  cu-  ft* 

The  area  of  the  steam-orifice  is  consequently 

2.781  X  11.15 

as  =  — -  -  =  0.00174  sq.  ft., 

12.7  X  1403 

and  the  diameter  is  0.55  of  an  inch. 

By  equation  (226)  the  area  of  the  water-orifice  is 

2.781  x  13.7 

*-  =  62.4  X  12.7  X  102.4  =  a°°°469  Sq'  ft" 

and  the  diameter  is  0.22  of  an  inch. 

Suppose  that  the  injector  ^vas  required  to  lift  20  feet,  then 
the  value  of  y  is  changed  but  little,  and  the  values  of  w  and  x^ 
not  at  all.  The  first  approximation  of  Fwill  be 


r=  _I4£L_+    /  _^-j  +20  I0g 

2  X   13.7  n      V     ^2  X   J3-7' 

which  gives  for  the  diameter  of  the  water-orifice  0.21  of  an  inch 
instead  of  0.22,  as  found  before. 

Limits  to  the  Action  of  an  Injector. — If  the  height  of  a 
water  column  equivalent  to  the  pressure  pl  in  the  boiler,  plus 
the  height  of  the  lift,  be  represented  by  h,  then  when 

772 
h<^ 

the  water  will  enter  the  boiler  with  a  residual  velocity.     If 

h  =  —  , (227) 

2 & 7  \         /  J 

the  water  will  enter  the  boiler  without  residual  velocity.  This 
fixes  the  limit  of  the  action  of  the  injector,  since  it  will  fail  to 
work  if 

F3 


INJECTORS.  153 

Injectors  are  commonly  tested  by  the  makers  under  the 
conditions  of  service,  with  the  pressure  in  the  delivery-  or  feed- 
pipe, 10  or  15  pounds  above  the  pressure  of  the  steam  supplied, 
to  insure  that  the  water-jet  shall  be  able  to  overcome  the  boiler- 
pressure  and  the  added  resistance  of  valves  and  pipes.  A  re- 
sidual velocity  is  accompanied  by  a  larger  delivery  by  the  in- 
jector and  a  higher  temperature,  and  when  the  injector  is  used 
to  feed  a  boiler  is  not  accompanied  by  any  loss  of  heat  or  en- 
ergy, radiation  and  friction  being  neglected. 

The  height  to  which  an  injector  will  lift  cold  water  depends 
on  the  form  and  proportions  of  the  parts  of  the  injector.  In- 
jectors are  seldom  set  to  lift  more  than  20  feet.  Since  hot 
water  gives  off  vapor  at  a  pressure  depending  on  its  tempera- 
ture, it  cannot  be  lifted  to  so  great  a  height  as  cold  water, 
either  by  an  injector  or  a  pump. 

The  temperature  of  feed-water  delivered  by  an  injector  is 
limited  by  the  fact  that  the  steam  used  must  be  condensed 
at  the  pressure  existing  in  front  of  the  steam-orifice.  The 
temperature  may  be  higher  with  a  small  lift  than  with  a  high 
lift,  and  may  be  increased  if  the  water  be  supplied  under 
pressure. 

The  temperature  of  the  water  in  the  reservoir  must  be  low 
enough  to  give  the  range  of  temperature  required  to  condense 
the  steam  used. 

A  pair  of  orifices  for  the  steam-  and  water-jets  of  an  injec- 
tor which  give  a  considerable  residual  velocity  with  a  range  of 
temperatures  well  within  the  limits,  will  continue  to  work  if  the 
conditions  be  changed,  but  a  limit  is  soon  reached  beyond  which 
the  injector  will  fail  to  act.  Beyond  the  limit  three  cases  may 
arise :  (a)  water  will  be  wasted  at  the  overflow ;  (&)  steam  will 
appear  at  the  overflow;  (c)  air  will  be  sucked  in  at  the  over- 
flow. In  the  last  case  the  air  drawn  in  may  break  the  continu- 
ity of  the  water-jet.  The  other  two  cases,  in  addition  to  the 
waste  pf  water  or  steam,  are  liable  to  interrupt  the  action  of 
the  injector.  They  are  certain  to  do  so  if  the  overflow-valve  is 
closed  after  the  injector  is  started. 

Fixed   Nozzle   Injector. — The  Mack   injector  shown  by 


154  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Figs.  30  and  31  is  of  this  type,  that  is,  the  water-  and  steam- 
orifices  are  both  fixed.  The  action  of  the  injector  is  controlled 
mainly  by  regulating  the  supply  of  steam  at  the  steam-valve, 
though  the  supply  of  water  may  be  reduced  within  limits  at  the 
water-valve.  The  overflow-valve  allows  water  or  steam  to 
escape,  but  prevents  air  from  entering.  When  the  steam  pres- 
sure is  low  or  there  is  a  head,  it  may  be  necessary  to  diminish 
the  supply  of  water. 

An  injector  of  this  type  has  been  known  to  feed  water  to  a 
boiler  with  both  water-  and  steam-valve  open,  and  with  steam 
escaping  at  the  overflow. 

Giffard  Injector. — This  is  the  oldest  form  of  injector  in 
which  the  steam-  and  water-orifices  were  both  adjustable.  It 
had  a  hollow  spindle,  through  which  steam  was  first  admitted 
to  induce  the  flow  of  water,  and  this  spindle  moving  inside  a 
hollow  cone  regulated  the  supply  of  steam.  The  hollow  cone 
was  also  movable,  so  that  by  it  the  water  space  surrounding  it 
could  be  controlled. 

Automatic  Injectors. — With  either  of  the  two  preceding 
examples  of  injectors,  the  change  of  boiler-pressure  is  liable 
to  require  a  regulation  by  hand,  lacking  which  the  inject- 
or may  stop.  In  some  forms  the  instrument  is  made  auto- 
matic, as,  for  example,  the  Sellers  injector  shown  by  Figs.  32 
and  33. 

A  is  the  receiving  or  steam  tube,  which  is  opened  or  closed 
by  the  valve  X.  Through  it  passes  a  hollow  spindle,  to  the 
inside  of  which  steam  is  admitted  by  the  valve  W,  which  ^can 
be  opened  without  raising  X  from  its  seat,  by  moving  the 
spindle  until  the  shoulder  just  touches  that  valve.  This  small 
motion  of  the  spindle  admits  steam  for  raising  water  till  it 
overflows  at  P.  When  this  occurs  the  spindle  is  drawn  back 
and  the  steam-valve  X  opened  wide,  upon  which  the  action 
should  be  complete  and  water  should  be  forced  into  the  boiler. 
The  rod  L  is  connected  to  the  handle  H  in  such  a  manner  as 
to  close  the  overflow  when  the  steam-valve  is  wide  open.  To 
diminish  the  amount  of  water  delivered  by  the  injector  the 
steam-valve  may  be  partially  closed. 


INJECTORS. 


FIG.  32. 


1 56  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


STEAM 


The    supply  of   water   is  controlled   automatically  by  the 
movable  piston  NN,  which  moves  freely  in  the  cylindrical  shell 

MM,  and  is  guided  also  at 
the  forward  end  ;  as  shown, 
it  is  as  far  forward  as  it  can 
go.  The  impact  of  the  wa- 
ter upon  the  piston  tends  to 
move  it  forward,  and  on  the 
other  hand  water  may  pass 
through  the  orifice  at  <9,  and 
produce  a  pressure  tending  to 
move  the  piston  backward. 
Thus  the  supply  of  water  is 
automatically  adjusted  to  the 
steam. 

Double  Injectors.  —  It 
was  remarked  that  the  tem- 
perature of  the  feed-water 
could  be  materially  increased 
in  an  ordinary  single  injector 
by  supplying  the  water  un- 
der a  head.  The  double  in- 
jector consists  of  two  parts, 
each  essentially  a  single  in- 
jector. The  first  part,  called 
the  lifter,  draws  water  from 
the  reservoir  and  forces  it 
into  a  chamber,  from  which 
the  second  part,  called  the 
forcer,  takes  it  and  forces  it 
to  the  boiler.  The  double 

injector  also  has  the  advantage  that  it  is  to  a  large  extent  self- 
regulating,  since  a  rise  of  boiler-pressure  which  increases  the 
flow  of  steam  through  the  forcer-jet  increases  the  flow  of  steam 
through  the  lifter-jet  in  like  manner,  and  thus  increases  the 
supply  of  water,  and  also  increases  the  pressure  in  the  inter- 
mediate chamber. 


INJECTORS. 


157 


All  double  injectors  are  fixed-nozzle  injectors  and  are  lifting 
injectors. 

Fig.  34  shows  the  Hancock  inspirator  in  section.  The  steam 
enters  at  £>  and  flows  to  the  lifter-jet  directly  beneath,  and  also 
supplies  the  forcer-jet  at  C,  where  there  is  a  valve  for  control- 
ling the  flow.  The  water  enters  at  A  and  is  delivered  by  the 
lifter  to  the  intermediate  chamber  D,  from  which  it  is  taken 
by  the  forcer  and  delivered  to  the  boiler.  At  I  is  a  valve 
connecting  the  intermediate  chamber  with  the  delivery,  and 
at  3  is  the  overflow-valve. 

To  start  the  inspirator,  close  2,  and  open  I  and  3.  Let  on 
steam,  and  when  water  appears  at  the  overflow  close  I.  Open 
2  a  quarter  of  a  turn,  and  then  close  the  overflow,  upon  which 
the  water  will  be  forced  to  the  boiler.  No  adjustment  is 
necessary  for  varying  steam-pressure,  but  the  quantity  and 
temperature  of  the  water  delivered  may  be  varied  by  varying 
the  steam-  or  water-supply. 


FIG. 


The  Korting  injector  is  shown  by  Figs.  35^  and  35^.     The 
arrangement  and  action  of  the  parts  is  evident  without  detailed 


158 


THERMODYNAMICS  OF  THE  STEAM-ENGINE. 


description.  The  handle  is  moved  a  short  distance  till  the 
lower  or  forcer  valve,  which  opens  first,  has  given  steam  to  the 
forcer,  and  water  appears  at  the  overflow.  Then  the  handle  is 


FIG.  356. 

pulled  back  as  far  as  it  will  go.  The  overflow  to  the  inter- 
mediate chamber  closes  when  the  forcer  is  started. 

The  Hancock  inspirator  is  also  arranged  to  work  by  one 
continuous  motion  of  a  handle,  when  it  is  applied  to  loco- 
motives. 

Tests  of  Injectors. — The  table  opposite  gives  the  results 
of  experiments  made  on  the  Sellers  self-adjusting  injector  hav- 
ing the  combining  tube  or  water-orifice  6  mm.  in  diameter  at 
the  smallest  section. 

For  each  pressure  of  steam  noted  in  column  I,  the  water 
was  delivered  by  the  injector  into  the  boiler  under  approx- 
imately the  same  pressure.  The  delivery  was  measured  by 
observing  the  indications  of  a  water-meter.  The  pressures  in 
column  8  were  obtained  by  throttling  the  steam  supplied  to  the 
injector,  and  observing  the  pressure  at  which  it  ceased  to  work, 
each  experiment  being  repeated  several  times  with  precisely 


INJECTORS. 


159 


EXPERIMENTS  ON  A  SELLERS  INJECTOR. 
(Diam.  Water-orifice  6  mm.) 


"8  £  «•« 

•o  ^ 

CO   U 

DELIVERY 

TEMPERATURE, 

II 

'§•« 

Ph* 

in  Cubic  Feet  per  Hour. 

Fahrenheit  Degrees. 

if  j 

4j  rt  M 

•*J? 

o  ^ 

•i 

Delivered  Water. 

s|| 

s| 

l^|| 

ii 

cQ 

1^3 

U-O 

an 

Q 

Its*" 

a 

p 

a 

3 

ai 

1 

ft 

s  . 

li 

*O   1>"* 

-*l 

Isll 

s 
1 

e 

'a 

|| 

1 

03  ^3 

a 

i| 

|o| 

III 

£ 

H 

§ 

& 

K 

2 

< 

Pu 

3 

I 

2 

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4 

5 

6 

7 

8 

9 

IO 

75-3 

63.6 

0.845 

66 

IOO 

94 

3 

132 

20 

82.4 

61.2 

0-743 

66 

108 

104 

9 

134 

30 

94.2 

56.5 

0.600 

66 

114 

116 

16 

134 

40 

100.  1 

60.0 

0-599 

66 

120 

123 

22 

132 

50 

108.3 

64.7 

0.597 

66 

124 

125 

27 

131 

60. 

116.5 

63.6 

0.546 

66 

I27 

133 

34 

130 

70 

124.8 

63.6 

0.510 

67 

I30 

142 

40 

130 

80 

i33-o 

67  .-i 

0-505 

66 

134 

144 

46 

131 

90 

i4i-3 

69-5 

0.492 

67 

136 

148 

52 

132 

100 

147.2 

64.7 

0.456 

66 

I40 

'59 

58 

132 

no 

i53-o 

67.1 

o-439 

67 

144 

162 

63 

132 

120 

156.6 

73-o 

0.466 

67 

I48 

162 

69 

134 

I30 

161.2 

74.2 

0.460 

66 

150 

165 

75 

130 

I40 

166.0 

78.9 

0.476 

66 

153 

166 

81 

126 

ISO 

170.7 

70.6 

0.414 

66 

157 

167 

88 

121 

the  same  results.  The  temperatures  in  column  9  were  obtained 
by  gradually  heating  the  water  supplied  to  the  injector,  and 
noting  the  temperature  at  which  it  ceased  to  operate,  each 
temperature  recorded  being  checked  by  several  repetitions  of 
the  experiment. 

Some  experiments  were  made  in  the  laboratory  of  the 
Institute  of  Technology,  by  Messrs.  Bradlee  and  Blanchard,* 
on  several  styles  of  injector,  of  which  the  results  are  given  in 
the  following  table : 


*  Thesis.     1888. 


160  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

'SUIUIUrT 


I 
«w 

£o 
<-o 


-uadxg  Xg 


N       <N 


•spunoj; 
jnop{  jad  pasn  uiBais 


•spunoj 
'anon 


•spanoj 
'anon 
pai[ddn 


--c>d     woovovd     p     •*    «/>    o 

lO^-^lOlO^^-V^VO       IOIOVO 


jo  saqouj  ui  aoijong 


•bg  jad  spunoj    |     ^t^0<?0(?^trt^9vc!°"0.  °° 


tvOO       OOOOOO       t»- 


MH       MM 
t^txt^t>- 


I3    =    f 

J  Q 


^  . 
• 

ffi 


INJECTORS,  l6l 

Sizes  of  Orifices. 

Hancock:  lifter,  steam,  .     .     .     .     .     .  0.114 

"  forcer,  steam,  ......  0.206 

"  "  water,  ......  0.149 

Lombard:  steam,  .     .....  0.224 

"  water,  ......  0.164 

Dodge:  steam,  .     .     .     .     .     .  0.161 

"  water,  ......  0.131 

The  experiments  15  to  21,  inclusive,  were  made  with  im- 
proved methods  of  reducing  the  evaporation  of  the  hot  water 
delivered  by  the  injector,  and  the  results  are  more  consistent 
and  reliable  than  the  preceding  ones.  It  is  apparent  that  the 
weight  of  steam  used,  which  is  obtained  by  taking  the  differ- 
ence between  the  weights  of  water  supplied  and  delivered,  is 
diminished  by  the  evaporation,  and  that  consequently  the 
experimental  quantity  of  water  delivered  by  one  pound  of 
steam  is  made  too  large  thereby  :  this  explains  part  of  the  dis- 
crepancy of  the  first  fourteen  experiments. 

The  calculations  for  Experiment  17  on  the  Dodge  injector, 
on  the  assumption  that  the  pressure  in  the  steam-orifice  is  O.6 
of  the  absolute  boiler-pressure,  are  as  follows  : 

Pressure  in  the  steam-orifice, 

0.6  X  86.2  —  51.7  pounds. 

Quality  of  steam  in  the  steam-orifice  on  the  assumption  of 
0.03  priming, 


0.97  X  891.8  , 

-  +  0-459'  =-'  +  04138; 


*,   =   0.94. 

Velocity  of  the  steam  in  the  steam-orifice, 


778  x  64.4  =      5-l27-3-  253.3; 
/.  w  =  1398  feet  per  second. 


1 62  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Specific  volume  of  steam  in  steam-orifice, 

v9  =  0.94  x  8.239  +  0.016  =  7.76. 
Flow  of  steam  in  pounds  per  second, 

7r(o.i6i)2  x  1398 
4x144x7.76     =  0-2547  pounds; 

Napier's  rule  gives  0.2509  pounds. 

The  flow  of  steam  per  hour  is  91.7  pounds  by  the  calcula- 
tion, instead  of  93.1  by  experiment. 
The  velocity  of  the  water-jet  is 

V  = —  =  126  feet  per  second. 

The  head  equivalent  to  74  pounds  per  square  inch  is 
74  X  144 


62.4 


=  170.7  feet. 


Adding,  in  the  lift,   10.4  feet,  gives  181.1  feet.     The  velocity 
required  to  overcome  this  head  is 


4/2  X  32.2  X   1 8 1. 1  =  1 08  feet  per  second. 

If  it  be  assumed  that  the  jet  in  the  water-orifice  is  entirely 
water,  then  the  velocity  calculated  from  the  weight  of  water 
delivered  per  hour  and  the  diameter  of  the  water-orifice  is 

1032.6  7r(.i3i)2 

-2 — i-2 i v        '   —  78  feet  per  second. 

3600  X  62.4       4  X  144 

From  these  calculations  it  appears  that  either  the  steam  is 
not  entirely  condensed  till  after  the  smallest  section  of  the  water- 
orifice  is  passed,  or  else  there  is  a  vena  contracta.  A  similar 
result  was  found  by  the  makers  of  the  Sellers  injector  for  some 
of  the  experiments  on  page  159. 

Exhaust-steam  Injectors. — It  has  been  pointed  out  that 
an  injector  may  be  made  to  deliver  water  against  a  pressure 
higher  than  the  pressure  of  the  steam  supplied.  An  extreme 


INJECTORS.  163 

example  of  this  is  found  in  injectors  which  use  the  exhaust 
steam  of  a  non-condensing  engine  for  feeding  a  boiler.  Such 
an  injector  must  be  supplied  with  cold  water  :  it  cannot  deliver 
water  at  a  high  temperature,  and  it  carries  with  it  some  of  the 
oil  from  the  engine  cylinder. 

The  Injector  as  a  Pump.  —  The  injector  is  commonly  used 
as  a  boiler-feeder,  in  which  office  it  may  be  advantageous  as  a 
feed-water  heater,  since  all  the  heat  not  expended  as  work  in 
forcing  the  water  into  the  boiler  is  returned  to  the  boiler  with 
the  water,  though  at  a  lower  temperature.  When  used  as  a 
pump,  to  deliver  water  against  a  head,  the  heat  given  to  the 
water  is  often  thrown  away,  and  may  be  prejudicial  ;  for  such 
work  the  injector  has  a  very  low  efficiency. 

Acids  and  solutions  are  sometimes  raised  by  injectors  of 
special  construction  made  to  resist  the  action  of  the  fluids. 

Let  the  height  of  one  reservoir  above  the  other,  through 
which  the  water  is  to  be  raised,  be  H\  then 


in  which  h  is  the  head  above  the  injector  and  s  is  the  distance 
the  water  is  lifted.  It  is  desirable  that  there  shall  be  little  or 
no  residual  velocity;  hence  by  equation  (227) 

V  =  V2gk. 
Equation  (221)  for  this  case  becbmes 


or,  substituting  for  V  from  the  equation  above,  and  reducing 

w  V2k  w  Vh 


An  inspection  of  equation  (228)  shows  that  the  quantity  of 
water  raised  per  pound  of  steam  increases  with  w,  which  de- 
pends on  the  steam-pressure  and  the  quality  of  the  steam,  but 
is  independent  of  the  pressure  in  front  of  the  orifice,  when  the 


164  FHERMODYNAMICS  OF    THE   STEAM-ENGINE. 

steam-pressure  is  more  than  fifteen  pounds  by  the  gauge.  The 
quantity  of  water  raised  per  pound  of  steam  decreases  with  the 
lift  h^  and  the  suction  s.  The  greatest  practical  lift  is  about 
26  feet. 

PROBLEM. — Required  the  number  of  pounds  of  water  raised 
per  pound  of  steam,  through  a  total  height  of  100  feet,  the 
injector  being  20  feet  above  the  lower  reservoir,  and  the  steam 
pressure  being  45  pounds  by  the  gauge. 

The  velocity  of  the  steam  w  is  1403  feet  per  second ;  con- 
sequently by  equation  (228) 

14031/80 

=  17-4; 


.%  y  =  16.4. 

If  the  total  height  were  50  feet,  then  the  number  of  pounds 
of  water  per  pound  of  steam  would  be  22.9. 
In  the  first  case  the  work  done  is 

16.4  X  100  =  1640  foot-pounds, 
and  in  the  second 

22.9  x  50  =  2290  foot-pounds. 

It  consequently  appears  that  it  is  more  economical  to  raise 
water  through  large  than  through  small  heights  by  this  method. 

The  following  calculation  shows  that  the  consumption  of 
steam  by  an  injector  used  as  a  pump  is  extravagant  when 
compared  with  a  pumping  engine.  Let  the  injector  be  sup- 
posed to  use  one  pound  of  steam  per  second ;  in  the  first  case 

1640 
its  horse-power  is ,  and  the  consumption  of   steam    per 

horse-power  per  hour  is 

550  x  60  x  60 

-  =  1 200  pounds. 
1640 


INJECTORS. 


i65 


In  the  second  case  the  consumption  is  1700  pounds  per 
horse-power  per  hour. 

When  the  injector  is  used  as  a  boiler-feeder  its  action  is 
first  that  of  a  pump, — in  which  its  efficiency,  as  has  been  seen,  is 
small, — and  second,  that  of  a  feed-water  heater ;  and  its  second 
action  is  useful  to  such  a  degree  as  an  independent  feed-water 
heater  using  boiler  steam  would  be.  Feed-water  may  some- 
times be  heated  by  exhaust  steam  or  by  hot  gases  beyond  the 
boiler,  in  which  case  heat  that  would  otherwise  be  wasted  is 
made  useful.  It  is  to  be  remarked  that  a  much  greater  gain 
would  result  from  the  substitution  of  a  condensing  engine,  in 
the  first  instance,  were  it  possible  to  do  so ;  and  that,  in  the 
second  instance,  it  is  difficult  to  properly  heat  feed-water  with 
the  gases  that  leave  an  economical  boiler. 

Water -inject  or. — Fig.  36  represents  a  device  called  a 
water-injector,  in  which  a  small  stream  of  water  in  the  pipe  M 


FIG.  36. 

flowing  from  the  reservoir  R  raises  water  from  the  reservoir  R" 
to  the  reservoir  R'. 

Let  one  pound  of  water  from  the  reservoir  R  draw  y  pounds 
from  R",  and  deliver  I  -\- y  pounds  to  R.  Let  the  velocity  of 
the  water  issuing  from  A  be  v ;  that  of  the  water  entering  from 
R"  be  z>a  at  N-  and  that  of  the  water  in  the  pipe  O  be  vim 
The  equality  of  momenta  gives 

(229) 


1  66  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

Let  x  be  the  excess  of  pressure  at  M  above  that  at  N  ex- 
pressed in  feet  of  water  ;  then 

v?  =  2gx  ; 


Substituting  in  equation  (229), 

j  +  j,  VJ  =  (i  +  y) 


(230) 

It  is  evident  from  inspection  of  the  equation  (230)  that/ 
may  be  increased  by  increasing  x ;  for  example,  by  placing  the 
injector  above  the  level  of  the  reservoir  so  that  there  may  be 
a  vacuum  in  front  of  the  orifice  A. 

If  the  weight  G  of  water  is  to  be  lifted  per  second,  then 

—  pounds  per  second  must  pass  the  orifice  A,  G  pounds  the 

space  at  N,  and  (i  -\-  y)G  pounds  through  the  section  at  O; 
which,  with  the  several  velocities  v,  vz  ,  and  vl  ,  give  the  data 
for  the  calculation  of  the  required  areas. 

PROBLEM. — Required  the  calculation  for  a  water-injector  to 
raise  1200  gallons  of  water  an  hour,  H  =  96  ft.,  h  =  12  ft., 
x  —  4  ft. 


V   =  V2  X  32.2  X  100  —  80. 


.25  feet  per  second; 

vl  =  \/2  X  32.2  x  16    =  32.10  feet  per  second; 

v^  =  |/2  X  32.2  X    4    =  16.05  feet  Per  second. 

I2OO  gallons  an  hour  =  0.04452  cubic  feet  per  second. 


INJECTORS.  167 

The  areas  are 

0.044^2 

a  =  -  —      —  0.000185  square  feet; 

3  X  80.25 


0.044^2 

#a  —      7^  =  0.00277  square  feet. 

The  diameters  corresponding  to  the  velocities  v  and  vl  are 

d  =  o.i  8  of  an  inch  ; 
di  —  0.58  of  an  inch. 

The  area  #„  is  of  annular  form,  having  the  area  0.4  of  a 
square  inch. 

Ejector.  —  The  investigation  of  the  injector  used  as  a  pump 
showed  it  to  be  a  very  wasteful  machine,  especially  when  the 
water  was  lifted  through  a  small 
height.  The  efficiency  is  much 
improved  by  arranging  the  instru- 
ment as  in  Fig.  37,  so  that  the 
steam  nozzle  A  shall  deliver  a 

small  stream  of  water  at  a  high  velocity,  which,  as  in  the  water- 
injector,  delivers  a  larger  stream  at  a  less  velocity.  Each  addi- 
tional conical  nozzle  increases  the  quantity  at  the  expense  of 
the  velocity,  so  that  a  large  quantity  of  water  may  be  lifted  a 
small  height. 

Ejectors  are  commonly  fitted  in  steamships  as  auxiliary 
pumps  in  case  of  leakage,  a  service  for  which  they  are  well 
fitted,  since  they  are  compact,  cheap,  and  powerful,  and  are 
used  only  in  emergency,  when  economy  is  of  small  conse- 
quence. 

Ejector-condensers.  —  When  there  is  a  good  supply  of 
cold  condensing  water,  an  exhaust-steam  injector,  using  all  the 
steam  from  the  engine,  may  be  arranged  to  take  the  place  of 
the  air-pump  of  a  jet-condensing  engine.  The  energy  of  the 
exhaust  steam  flowing  from  the  cylinder  of  the  engine  to  the 


1  68  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

combining  tube,  where  the  absolute  pressure  is  less  and  where 
the  steam  is  condensed,  is  sufficient  to  eject  the  water  and  the 
air  mingled  with  it  against  the  pressure  of  the  atmosphere,  and 
thus  to  maintain  the  vacuum. 

PROBLEM.  —  Suppose  that  the  absolute  pressure  in  the  cylin- 
der of  an  engine  is  4  pounds  absolute,  and  the  pressure  in 
the  steam-orifice  of  an  ejector-condenser  is  2  pounds  absolute  : 
find  the  pounds  of  condensing  water  per  pound  of  steam  and 
the  velocity  of  the  water-jet.  Let  the  exhaust  steam  contain 
ten  per  cent  of  moisture,  then  the  velocity  of  the  steam-jet  is 
obtained  from 

Aw*      o.o  x  1007.2  , 

1%  =613.8       (I53'°9  ~  126.3)4-587(0.2203  -  0.1754) 

+  121.4  —  94.4  =  69.2; 
,\  w  =  1300  feet  per  second,  nearly  ; 

_Q.9X  1007.2  +12  1.  4-  944  _ 
68.01  -  28.12 


22  -f-  I 

The   velocity   required    to   overcome  the  pressure  of  12.7 
pounds  per  square  inch  is  43  feet  per  second. 


EXAMPLES. 

1.  In  the  problem  given    on  page    151    suppose   that  the 
steam  contains  10  per  cent  of  moisture  and  make  all  the  re- 
quired calculations. 

2.  In  the  same  problem  let  the  lift  be  10  feet  and  make  all 
calculations,  the  steam  having  5  per  cent  of  moisture. 

3.  An  injector  which  feeds  a  boiler  having  a  pressure  of  6 
atmospheres  takes  feed-water  at  20°  C,  and  delivers  it  at  80° 
C.     How  many  kilograms  of  steam  are  fed  by  one  kilogram  of 
water? 


INJECTORS.  169 

4.  An  injector  which  feeds  a  boiler  having  a  pressure  of  100 
pounds  by  the  gauge  delivers   1 6  pounds  of  water  for  each 
pound  of  steam :  the  initial  temperature  of  the  feed-water  is  40° 
C;  what  is  the  final  temperature?     No  lift  nor  head. 

5.  Suppose  an  injector  is  used  to  supply  an  ether  vaporizer 
in  which  the  temperature  is   100°  C.,  how  many  kilograms  of 
liquid  will  be  delivered  per  kilogram  of  dry  vapor,  when  the 
initial  and  final  temperatures  of  the  liquid  fed  are  10°  C.  and 
50°  C? 

6.  Suppose  that  an  injector  supplied  with  dry  steam  at  3 
atmospheres  is  used  to  pump  chloroform  against  a  head  of  30 
metres  of  the  liquid.     How  many  kilograms  of  liquid  will  be 
delivered  by  one  kilogram  of  steam  if  the  initial  and  final  tem- 
peratures of  the  liquid  are  o°  and  20°  C.  ? 

7.  An  exhaust  steam-injector  is   supplied    with   steam   at 
atmospheric  pressure.     How  many  pounds  of  water  per  pound 
of  steam  will  it  deliver  to  a  boiler  at  a  pressure  of  60  pounds  by 
the  gauge,  the  initial  and  final  temperatures  of  the  feed-water 
being  40°  and  80°  F.  ? 

8.  An  injector  is  used  to  pump  water  against  a  head  of  100 
feet,  it  is  set  20  feet  above  the  cistern,  and  is  supplied  with  dry 
steam  at  80  pounds  gauge  pressure.     How  many  pounds  of 
water  will  be  raised  per  pound  of  steam  ?     What  is  the  con- 
sumption of  steam  per  horse-power  per  hour?     If  the  initial 
temperature  of   the   feed-water  is  60°  F.,  what  will  the  final 
temperature  be?     What  is  the  efficiency  of  the  instrument  as 
a  heat-engine  ? 


CHAPTER   XI. 

HOT-AIR     ENGINES. 

Engines  of  Maximum  Efficiency. — In  order  to  have  the 
maximum  efficiency,  an  engine  must  work  on  such  a  cycle  that 
its  working  substance  shall  always  have  the  temperature  of  the 
source  of  heat  when  acquiring  heat,  and  the  temperature  of 
the  refrigerator  when  rejecting  heat ;  that  is,  the  engine  must 
be  reversible. 

The  older  forms  of  hot-air  engines  all  had  the  source  of 
heat  at  one  constant  temperature  and  the  refrigerator  at  an- 
other lower  constant  temperature.  To  have  the  maximum 
efficiency  it  was  required  that  the  working  substance  should 
receive  heat  from  external  sources  at  one  temperature,  and 
reject  heat  to  external  sources  at  one  temperature  only. 

Carnot's  engine  is  the  only  simple  engine  which  can  fulfil 
these  conditions  when  air  is  the  working  substance.  The  cycle 
of  that  engine  has  never  been  adopted  in  practice,  since  it 
involves  incompatible  requirements ;  that  is,  the  isothermal 
changes  should  be  very  slow  and  the  adiabatic  changes  should 
be  very  rapid,  to  make  the  cycle  of  an  actual  engine  approxi- 
mate to  the  ideal  cycle. 

By  aid  of  a  device  called  a  regenerator  or  economizer,  actual 
engines  have  been  made  which  have  an  ideal  cycle  of  maximum 
efficiency.      Such   a  cycle   is  represented   by 
Fig.  38.     The  curves  DC  and  AB  are  isother- 
mals,  which  form  those  parts  of  the  cycle  dur- 
ing which  heat  is  received  from  the  source 
and  rejected  to  the  refrigerator.     The  curves 
BC  and  DA  correspond  to  the  adiabatic  lines 
—  of  Carnot's  cycle,  and  must  fulfil  the  one  con- 
dition, that  the  heat  given  to  the  regenerator 
during  one  operation,  as  that  represented  by  BC,  must  be  equal 

170 


HOT-AIR  ENGINES.  I?  I 

to  the  heat  received  from  the  regenerator  during  the  converse 
operation  DA. 

The  relation  between  the  curves  BC  and  DA  may  be  de- 
termined as  follows  :  Let  the  equations  to  BC  and  AD  be 


then  by  aid  of  the  characteristic  equation  of  the  working  sub- 
stance, 

/(A  v,  ')  =  o, 
v  may  be  eliminated,  giving 


for  the  equations  of  the  curves. 

Draw  the  intermediate  isothermals  XZ  and  Z^Fwith  a  dif- 
ference of  temperature  dt  ;  then  the  heat  received  by  one  unit 
of  weight  of  the  substance  in  passing  from  W  to  X  is 

dQ  —  cpdt  +  mdp,    ......     (230) 

and  that  rejected  from  ^to  Fis 

dQ=.cpdt  +  mfdpf  .......     (231) 

The  conditions  of  the  problem  will  be  fulfilled  by  making 
equation  (230)  equal  to  equation  (231),  so  that 

mdp  =  m'dp'. 

Substituting  for  m  from  equation  (53)  gives 
idv\  {dv'\ 

(*),*=(*),*'• 

Deducing  the  values  of  the  partial  differential  coefficients 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


from  the  characteristic  equation  for  a  gas,  and  substituting,  we 
have 


R 


R 


^_ 
P  ~~~~  P'  ' 


(232) 


That  is,  the  required  relation  is  that  the  ratio  of  the  pressures 
at  the  points  cut  by  any  isothermal  from  the  paths  DA  and 
BC  must  be  constant. 

Stirling's  Engine. — This  engine  was  invented  in  1816,  and 
was  used  with  good  economy  for  a  few  years,  and  then  rejected 
because  the  heaters,  which  took  the  place  of  the  boiler  of  a 
steam-engine,  burned  out  rapidly.  It  is  described  and  its  per- 
formance given  in  detail  by  Rankine  in  his  Steam-engine.  An 
ideal  sketch  is  given  by  Fig.  39.  E  is  a  dis- 
placer  piston  filled  with  non-conducting  ma- 
terial, and  working  freely  in  an  inner  cylin- 
der. Between  this  cylinder  and  an  outer  one 
from  A  to  C  is  placed  a  regenerator  made 
of  plates  of  metal,  wire  screens,  or  other  ma- 
terial, so  arranged  that  it  will  readily  take 
heat  from  or  yield  heat  to  air  passing  through 
it.  At  the  lower  end  both  cylinders  have  a 
hemispherical  head  ;  that  of  the  outer  cylin- 
der is  exposed  to  the  fire  of  the  furnace,  and 
that  of  the  inner  is  pierced  with  holes  through  which  the  air 
streams  when  displaced  by  the  plunger.  At  the  upper  end 
there  is  a  coil  of  pipe  through  which  cold  water  flows.  The 
working  cylinder  H  has  free  communication  with  the  upper 
end  of  the  displacer  cylinder,  and  consequently  it  can  be  oiled? 
and  the  piston  may  be  packed  in  the  usual  manner,  since  only  ;* 
cool  air  enters  it. 

In  the  actual  engine  the  cylinder  H  is  double-acting,  and 


HOT-AIR  ENGINES.  1/3 

there  are  two  displacer  cylinders,  one  for  each  end  of  the  work- 
ing cylinder. 

If  we  neglect  the  action  of  the  air  in  the  clearance  of  the 
cylinder  H  and  the  communicating  pipe,  we  have  the  following 
ideal  cycle.  Suppose  the  working  piston  to  be  at  the  begin- 
ning of  the  forward  stroke,  and  the  displacer 
piston  at  the  bottom  of  its  cylinder,  so  that  we 
may  assume  that  the  air  is  all  in  the  upper 
part  of  that  cylinder  or  in  the  refrigerator, 
and  at  the  lowest  temperature  7"a  ,  the  condi- 
tion of  one  pound  of  air  being  represented 
by  the  point  D  of  Fig.  40.  The  displacer 


piston  is  then  moved  quickly  by  a  cam  to 
the  upper  end  of  the  stroke  ;  while  the  working  piston  moyes 
so  little  that  it  may  be  considered  to  be  at  rest.  The  air  is 
thus  all  driven  from  the  upper  end  of  the  displacer  cylinder 
through  the  regenerator,  from  which  it  takes  up  heat  aban- 
doned during  the  preceding  return  stroke,  thereby  acquiring 
the  temperature  7^  ,  and  enters  the  lower  end  of  that  cylinder. 
During  this  process,  the  line  AD  of  constant  volume  is  de- 
scribed on  Fig.  40.  When  this  process  is  complete,  the  work- 
ing cylinder  makes  the  forward  stroke,  and  the  air  expands  at 
constant  temperature,  this  part  of  the  cycle  being  represented 
by  the  isothermal  AB  of  Fig.  40.  At  the  end  of  the  forward 
stroke  the  displacer  piston  is  quickly  moved  down,  thereby 
driving  the  air  through  the  regenerator,  during  which  process 
heat  is  given  up  by  the  air,  into  the  upper  part  of  the  displacer 
cylinder  ;  this  is  accompanied  by  a  cooling  at  constant  volume, 
represented  by  the  line  BC.  The  working  piston  then  makes 
the  return  stroke,  compressing  the  air  at  constant  temperature, 
as  represented  by  the  isothermal  line  CD,  and  completing  the 
cycle. 

To  construct  the  diagram  drawn  by  an  indicator,  we  may 
assume  that  in  the  clearance  of  the  cylinder  H,  the  communi- 
cating pipe,  and  refrigerator  there  is  a  volume  of  air  which 
flows  back  and  forth  and  changes  pressure,  but  remains  at  the 
temperature  Tt  .  If  we  choose,  we  may  also  make  allowance  for 


1/4  THERMODYNAMICS  OF  THE   STEAM-ENGINE. 

a  similar  volume  which  remains  in  the  waste  spaces  at  the 
lower  end  of  the  displacer  cylinder,  at  a  constant  tempera- 
ture 7;. 

In  Fig.  41,  let  ABCD  represent  the  cycle  of  operations, 
without  any  allowance  for  clearance  or  waste  spaces;  the 
minimum  volume  will  be  that  displaced  by  the  displacer  pis- 

ton, while  the  maximum  volume  is 
larger  by  the  volume  displaced  by  the 
working  piston.  Let  the  point  E 
represent  the  maximum  pressure,  the 
same  as  that  at  A  ;  and  the  united 
volumes  of  the  clearance  at  one  end 
of  the  working  cylinder,  of  the  com- 
FlG-  4I-  municating  pipe,  of  the  clearance  at 

the  top  and  bottom  of  the  displacer  cylinder,  and  the  volume 
in  the  refrigerator  and  regenerator.  Each  part  of  this  com- 
bined volume  will  have  a  constant  temperature,  so  that  the 
volume  at  different  pressures  will  be  represented  by  the  hyper- 
bola EF.  To  find  the  actual  diagram  A'B'CD',  draw  any 
horizontal  line,  as  sy,  cutting  the  true  diagram  at  u  and  v,  and 
the  hyperbola  EF  at  t  ;  make  ux  and  vy  equal  to  st  ;  then  x 
and  y  are  points  of  the  actual  diagram.  The  indicator  will 
draw  an  oval  similar  to  A'B'C'D'  with  the  corners  rounded. 

To  show  that  the  diagram,  Fig.  40,  fulfils  the  condition  for 
maximum  efficiency,  draw  an  intermediate  isothermal  XY. 
Since  DA  and  BC  are  lines  of  constant  volume, 


Tc 


The  diagram  in  Fig.  42  was  reduced  from  an  indicator-card 
from  a  recent  hot-air  engine  made  on  the  same  principle  as 
Stirling's  hot-air  engine.  To  avoid  destruction  of  the  lubricant 
in  the  working  cylinder  Stirling  found  it  advisable  to  connect 
only  the  cool  end  of  the  displacer  cylinder  with  the  work- 


HOT-AIR  ENGINES.  1/5 

ing  cylinder,  and  had  two  displacer  cylinders  for  one  working 
cylinder.     It  has  been  found  that  a  good  mineral  oil  can  be 
used  to  lubricate  the  displaced  pis- 
ton of  the  new  engine,  and   that 
the  hot  end  also  of  the  displacer 
piston  can  be  advantageously  con- 
nected with  the  working  cylinders, 

of  which  there  are  two.    Thus  each  FlG>  42> 

working  cylinder  is  connected  with  the  hot  end  of  one  dis- 
placer cylinder  and  with  the  cool  end  of  the  other  displacer 
cylinder. 

The  distortion  of  the  diagram  Fig.  42  is  due  in  part  to  the 
large  clearance  and  waste  space,  and  partly  to  the  fact  that  the 
displacer  pistons  are  moved  by  a  crank  at  about  70°  with  the 
working  crank. 

Ericsson's  Engine. — This  engine  consists  essentially  of  a 
working  cylinder,  a  compressing  pump,  and  a  reservoir.  To 
give  a  perfect  ideal  cycle,  a  regenerator  and  a  refrigerator  are 
required.  The  pump,  which  must  have  a  water-jacket  which 
acts  as  a  refrigerator,  draws  air  from  the  atmosphere  at  con- 
stant pressure,  compresses  it  at  constant 
temperature,  and  forces  it  into  the  reser- 
voir under  constant  pressure.  The  pump 
cycle  is  represented  by  the  diagram  EDAF 
(Fig.  43).  The  engine  draws' air  from  the 
reservoir  through  the  regenerator,  during 
which  process  it  is  heated  from  the  tern-  FlG-  «• 

perature  7^  to  Tl ;  the  supply  is  then  cut  off  by  a  slide-valve, 
and  the  air  in  the  cylinder  expands  at  constant  temperature 
down  to  the  atmospheric  pressure.  On  the  return  stroke  the 
air  is  forced  from  the  cylinder  at  constant  pressure  through  the 
regenerator,  being  thereby  cooled  to  the  temperature  T^.  The 
engine  cycle  is  represented  by  the  diagram  FBCE.  The  dia- 
gram of  effective  work  is  ABCD,  which  fulfils  the  condition  of 
maximum  efficiency,  since  AD  and  BC  are  isothermals,  and 
AB  and  CD  are  lines  of  constant  pressure. 

The  actual  engine  does  not  expand  down  to  the  atmospheric 


F  A 


\  V 

\ _VsJ 


176  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

pressure,  so  that  the  diagram  is  cut  short  by  a  line  like  GH. 
Also,  the  clearances  of  the  two  cylinders  introduce  irregularities 
and  modifications  of  the  diagram. 

Gas-engines. — The  various  forms  of  gas-engines  in  common 
use  are  hot-air  engines,  in  which  the  air  is  heated  by  the  com- 
bustion of  gaseous  fuel  mixed  with  the  air.     At  full  power 
there  is  one  working  stroke  for  two  revolutions,  the  engines 
being  single-acting.     Fig.  44  gives  the  cycle 
commonly  employed.     At  the  end  of  the 
working  stroke  the  pressure  suddenly  falls 
to  that  of  the  atmosphere,  and  on  the  re- 
turn stroke  the  gases  in  the  cylinder  are  ex- 
pelled at  atmospheric  pressure.     On  the  for- 
v  ward  stroke  the  new  charge  of  an  explosive 


FIG.  44.  mixture  of  gas  and  air  is  introduced,  and  on 

the  return  stroke  the  charge  is  compressed.  These  three  opera- 
tions are  represented  by  CE,  EC,  and  CD.  At  the  end  of  the 
compression  stroke  the  charge  is  ignited,  and  the  air  and  gases 
are  heated  at  constant  volume  by  a  very  rapid  combustion  or 
explosion.  During  the  forward  stroke  the  gases  resulting  from 
the  explosion  expand,  doing  work.  The  two  operations  com- 
pleting the  cycle  are  represented  by  DA,  AB.  The  cylinder  is 
kept  cool  by  circulation  of  water  to  prevent  its  destruction  by 
the  intense  heat  of  the  explosion.  This  cooling  influences  both 
expansion  and  compression  curves ;  also  the  expansion  curve  is 
modified  by  the  fact  that  the  explosion  is  not  instantaneous, 
but  continues  throughout  nearly  the  whole  of  the  forward 
stroke. 

The  efficiency  of  this  cycle,  on  the  assumption  of  instanta- 
neous explosion  and  adiabatic  expansion  and  compression,  is 
easily  found.  For  the  works  of  expansion  and  compression  we 
have 


HOT-AIR  ENGINES.  1  77 

Ta 

But  va  —  vd,     vb  =  vc,     pa  =  -^~  pd, 

1  d 

and  the  heat  given  to  the  gases  by  explosion,  if  c,  is  the  mean 
specific  heat  of  the  mixture  at  constant  volume,  is 


(K-  l)c,(Ta-  Td) 


(233) 


The  remarkable  conclusion  from  this  last  equation  is  that 
the  efficiency  for  such  a  cycle  does  not  depend  on  the  differ- 
ence of  temperatures,  but  rather  on  the  degree  of  expansion  and 
compression. 

NOTE.—  For  a  full  discussion  of  the  theory  and  practice  of  gas-engines  refer 
to  D.  Clerk's  Gas-engines. 


CHAPTER   XII. 

THE      STEAM-ENGINE. 

Carnot's  Cycle. — In  the  steam-engine  the  source  of  heat 
is  ultimately  the  fire  of  the  furnace,  but  the  heat  received  by  the 
engine  is  communicated  at  the  temperature  due  to  the  steam- 
pressure  in  the  boiler.  In  like  manner  the  lower  temperature 
is  that  due  to  the  pressure  of  the  vapor  in  the  condenser,  or,  if 
none  is  used,  it  is  the  temperature  of  boiling-point  under  at- 
mospheric pressure.  Consequently  heat  is  received  and  reject- 
ed at  constant  temperature ;  and  as  a  regenerator  cannot  be 
used,  the  only  cycle  of  perfect  efficiency  is  Carnot's  cycle.  The 
advantage  to  be  derived  from  the  discussion  of  this  cycle  is  that 
from  it  the  maximum  performance  of  steam-engines  may  be 
calculated  from  laboratory  experiments  only, 
which  experiments  are  susceptible  of  a  de- 
gree of  refinement  impossible  with  engine  ex- 
periments. The  efficiency  of  actual  engines 
L  is  always  inferior  to  that  of  Carnot's  cycle, 
because  the  cycle  of  such  an  engine  is  incom- 
plete  and  non-reversible,  and  there  are  un- 
avoidable losses  from  friction,  leakage,  and 
loss  of  heat. 

Let  Fig.  45  represent  the  cylinder  of  Car- 
not's engine,  using  M  pounds  of  a  mixture  of  steam  and  water, 
together  with  the  cycle  of  operations.  Beginning  at  the  point 
a,  the  cycle  is  as  follows : 

(i)  Expansion  at  constant  temperature  and  pressure,  repre- 
sented by  ab,  during  which  some  of  the  water  is  vaporized,  and 
the  heat  absorbed  is 

Q,  =  Mrfa  -  O.     ......     (234) 

178 


STEAM-ENGINE. 

(2)  Expansion  without  communication  of  heat,  represented 
by  the  adiabatic  be,  till  the  temperature  is  reduced  from  Tl  to 
Tz  .  This  expansion  is  accompanied  by  a  condensation  of  steam, 
so  that  xb  becomes  #e,  which  may  be  calculated  by  the  equa- 
tion 


(235) 


(3)  Compression  at  constant  temperature  and  pressure,  repre- 
sented by  cd,  during  which  steam  is  condensed  and  heat  is  re- 
jected to  the  amount 

Q9  =  Mr,(xe-xd)  .......     (236) 

(4)  Compression  without  communication  of  heat,  represent- 
ed by  da,  till  the  temperature  is  raised  from  Tt  to  T1  and  the 
cycle  is  completed.     For  this  operation  we  have 


..    (237) 


Equations  (235)  and  (237)  give 

*.-^  =  -r  4  <*,-*,)!  .......    (238) 

'  a     •*  i 
•*  i 

The  efficiency  is  therefore 

AW      &  -  &       T,-T, 

-&'•    -QT      -?r~' (240) 

and  the  effective  work  is 

w=-r    Jr    a=     r-x*-xJ    -~    \  t  .   (24I) 

SI  1  .  jTL  J.  . 


i8o 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


It  is  convenient  for  calculation  to  assume  that  at  the  begin- 
ning of  the  expansion  represented  by  ab  the  mixture  is  all 
water,  and  that  at  the  end  it  is  all  steam,  so  that  xa  =  o  and 
xb  =  I.  This  assumption  gives 


A 
AW 


(242) 
(243) 


To  find  the  water  evaporated  per  horse-power  per  hour  in 
such  an  engine,  make    W  equal  to  60  X  33,000  foot-pounds, 

and  substitute  for  A  its  value,  —  -  ,  which  gives  the  expression 


775 


60^X33000 


-  •  (244) 


The  following  table  was  calculated  by  aid  of  equations  (240) 
and  (241).  The  lower  temperature  for  non-condensing  engines 
is  that  of  boiling-point  of  water  under  atmospheric  pressure  ; 
for  condensing  engines  it  depends  on  the  perfection  of  the 
vacuum  maintained  in  the  condenser,  which  was  assumed  in 
these  calculations  to  be  1.5  pounds  of  absolute  pressure.  It 
should  be  remarked  that  the  ratio  of  the  steam  consumption  of 
two  cycles,  actual  or  ideal,  is  not  necessarily  the  ratio  of  the 
efficiencies. 

EFFICIENCY   AND    CONSUMPTION   OF   A    PERFECT   STEAM- 

ENGINE. 


CONDENSING  ENGINES. 

NON-CONDENSING  ENGINES. 

Initial  Pressure 

by  the  Gauge, 
above  the 
Atmosphere. 

Efficiency 

ii  -  •  r, 

Ti 

Pounds  of  Steam 
per  H.  P. 
per  Hour. 

Efficiency 
Ti-7-, 

Pounds  of  Steam 
per  H.  P. 
per  Hour. 

r. 

15 

o.iSq 

14-3 

0.053 

50.9 

30 

0.215 

12.8 

0.084 

32.8 

60 

0.249 

ii.  4 

0.124 

22.9 

IOO 

0.278 

10.5 

0.157 

18.4 

150 

0.302 

9.8 

0.186 

16.0 

200 

0.320 

9-5 

0.207 

14-6 

300 

0.347 

9.0 

0.238 

I3-I 

STEAM-ENGINE.  1 8 1 

Equation  (241)  shows  that  the  latent  heat  of  evaporation  is 
a  measure  of  the  amount  of  work  that  one  unit  of  weight  of  a 
vapor  can  do  in  an  engine  ;  the  larger  the  latent  heat,  the  more 
the  work  per  pound  will  be.  Equation  (240)  shows  that  the 
efficiency  does  not  depend  on  the  latent  heat  nor  on  any  other 
property  of  the  working  substance,  as  was  shown  in  the  second 
law  of  thermodynamics,  of  which  this  is  a  special  case. 

A  comparison  of  Carnot's  cycle  for  the  steam-engine  in  Fig. 
45  with  that  of  Carnot's  cycle  for  an  air-engine,  Fig.  23,  shows 
that  the  chief  difference  is  that  the  isothermal  for  a  mixture  of 
a  liquid  and  its  vapor  is  a  straight  line,  while  that  of  a  gas  is  a 
hyperbola.  In  both,  the  heat  is  received  and  rejected  during 
isothermal  expansion  and  isothermal  compression  only.  In  the 
steam-engine  the  latent  heat  of  vaporization  is  the  property  by 
means  of  which  heat  is  received  and  rejected.  In  the  air-en- 
gine the  latent  heat  of  expansion  plays  the  same  part.  The 
fact  that  the  latent  heat  of  vaporization  of  steam  is  large,  per- 
mits the  steam-engine  cylinder  to  be  smaller  than  that  of  a  hot- 
air-engine  cylinder,  though  the  true  comparison  of  two  such  en- 
gines should  include  the  weight  and  bulk  of  the  whole  appara- 
tus, including  for  the  steam-engine  the  boiler  and  condenser. 

The  old  fallacy  that  the  latent  heat  of  vaporization  of 
steam  is  the  source  of  a  loss  that  can  be  avoided  by  an  engine 
using  a  substance  which,  like  air,  has  no  change  of  state,  and 
hence  no  latent  heat  of  vaporization,  is  apparent.  The  latent 
heat  yielded  by  the  steam  to  the  condensing  water  is  indeed 
large  ;  but  it  is  an  unavoidable  loss,  and  an  essential  action  of 
a  heat-engine. 

The  Actual  Engine. — The  cycle  of  all  actual  steam-en- 
gines is  quite  different  from  Carnot's  cycle,  and,  as  will  be  seen, 
it  always  has  a  less  efficiency.  Steam  is  generated  in  a  boiler 
at  constant  pressure,  and  is  carried  to  the  engine  through  a 
pipe  of  more  or  less  length,  suffering  in  transit  a  loss  of  heat  by 
radiation  and  a  loss  of  pressure  from  friction.  This  steam  is 
admitted  to  the  cylinder  for  a  portion  of  the  stroke,  during 
which  time  work  is  done  by  an  isothermal  expansion  of  the 
water  and  steam  in  the  boiler.  At  the  same  time  the  entering 


1 82  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

steam  yields  heat  to  the  walls  of  the  cylinder  and  suffers  partial 
condensation.  After  a  portion  of  the  stroke  the  supply  of  the 
steam  is  shut  off,  and  the  steam  in  the  cylinder  expands,  doing 
work.  In  general,  the  walls  of  the  cylinder  give  heat  to  the 
water  previously  condensed,  causing  a  partial  reevaporation,, 
though  sometimes  the  walls  receive  heat  during  a  part  or  the 
whole  of  the  expansion.  Near  the  end  of  the  stroke  the  com- 
munication is  opened  with  the  condenser,  and  the  steam  quick- 
ly falls  nearly  to  the  constant  pressure  maintained  in  the  con- 
denser ;  when  the  expansion  is  carried  so  far  as  to  reduce  the 
pressure  to  that  of  the  back  pressure,  the  cycle  is  complete  at 
this  part;  otherwise,  it  is  incomplete.  During  the  return  stroke 
the  piston  expels  the  steam  in  the  cylinder  to  the  condenser, 
and  the  walls  yield  heat  to  the  steam  and  water  in  the  cylinder, 
nearly,  if  not  completely,  evaporating  all  the  water  remaining. 
Towards  the  end  of  the  stroke  the  communication  with  the 
condenser  is  interrupted,  and  the  steam  remaining  in  the  cylin- 
der is  compressed,  and  the  temperature  and  pressure  are  raised. 
During  the  compression  heat  may  be  yielded  by  the  steam  to 
the  walls,  or  conversely,  depending  on  the  extent  of  compres- 
sion, and  on  whether  a  steam  jacket  is  used  or  not.  If  the  com- 
pression be  carried  so  far  that  the  pressure  is  raised  to  the  ini- 
tial pressure,  the  cycle  is  complete  at  this  part ;  otherwise,  it 
is  not.  Just  before  the  end  of  the  stroke  steam  is  admitted  in 
anticipation  of  the  next  stroke. 

The  water  resulting  from  the  condensation  of  steam  in  the 
condenser  is  returned  to  the  boiler  by  the  air-pump  and  feed- 
pump, thereby  forming  a  closed  cycle  of  operations.  The  air- 
pump  is  required  to  remove  the  air  which  enters  the  boiler  with 
the  feed-water,  and  passes  with  the  steam  through  the  engine 
and  into  the  condenser.  If  there  were  no  air  admitted  to  the 
boiler,  engine,  or  condenser,  with  the  feed-water  or  by  leakage, 
one  pump  might  take  the  water  from  the  condenser  and  return 
it  to  the  boiler.  When  a  surface  condenser  is  used,  the  same 
water  is  returned  to  the  boiler  and  used  continuously,  thereby 
forming  a  true  closed  cycle.  When  a  jet  condenser  is  used, 
the  steam  and  condensing  water  mingle,  and  are  removed  to- 


S  TEA  M -ENGINE.  1 8  3 

gether  by  the  air-pump  to  the  hot  well,  whence  the  feed-water 
is  drawn  ;  but  the  effect  is  the  same  as  though  the  same  water 
was  returned  to  the  boiler.  When  no  condenser  is  used,  the 
steam  escapes  into  the  air,  and  the  feed-water  is  drawn  from  a 
well  or  reservoir,  the  chief  difference  being  then  that  there  is  a 
wide  difference  of  temperature  between  the  steam  rejected 
and  the  water  which  replaces  it. 

The  cycle  described  is  clearly  non-reversible.  Heat  is  lost 
by  radiation  during  every  part  of  the  process,  even  when  pre- 
cautions are  taken  to  prevent  such  loss.  Also  heat  is  given 
to  the  cylinder  at  a  high  temperature  during  admission,  and  is 
restored  at  a  varying  but  lower  temperature  during  expansion, 
and  the  heat  given  by  the  walls  of  the  cylinder  during  the  ex- 
haust'is  thrown  into  the  condenser  without  compensation. 

Considering  the  furnace,  boiler,  engine,  and  condenser  as 
one  apparatus,  the  maximum  temperature  is  that  of  the  fire, 
and  the  minimum  that  of  the  cooling  water  ;  but  in  considering 
the  cycle  of  the  cylinder,  the  highest  temperature  is  that  due 
to  the  pressure  in  the  boiler,  and  the  lowest  that  due  to  the 
pressure  in  the  condenser. 

When  the  expansion  and  compression  are  carried  far  enough 
so  that  the  cycle  is  complete,  the  indicator-diagram  is  similar 
to  that  of  Carnot's  cycle,  Fig.  45  ;  but  the  expansion  and  com- 
pression curves  are  not  adiabatics.  If  a  non-conducting  cylin- 
der could  be  used,  the  cycle  would  still  differ  from  Carnot's 
cycle,  on  account  of  the  action  of  the  air-  and  feed-pumps,  and 
because  the  feed-water  is  heated  from  the  lower  to  the  higher 
temperature  in  the  boiler,  instead  of  having  that  change  of  tem- 
perature produced  by  compression. 

A  complete  working  theory  of  the  steam-engine  should  take 
account  of  all  of  the  actions  named,  including  the  action  of  the 
walls  of  the  cylinder,  the  incomplete  expansion  and  compression, 
the  losses  from  radiation  and  friction,  the  action  of  the  feed- 
and  air-pumps,  and  the  effect  of  the  clearance  or  waste  space  at 
the  ends  of  the  cylinder. 

Theories  have  been  proposed  by  Rankine,  Clausius,  Zeuner, 
and  others,  which  include  most  of  the  actions  mentioned,  but 


1 84  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

the  exchange  of  heat  between  the  walls  of  the  cylinder  and  the 
steam  is  in  no  case  included  in  such  theories.  Rankine*  states 
the  effect  of  water  in  the  clearance  space,  and  says  that  the 
thermal  action  of  the  walls  of  the  cylinder  has  the  same  effect ; 
but  he  makes  no  attempt  at  an  estimation  of  the  effect.  Zeuner,f 
in  connection  with  the  discussion  of  the  adiabatic  curve  of  a 
mixture  of  water  and  steam,  admits  the  thermal  action  of  the 
walls,  but  asserts  that  the  effect  has  been,  over-estimated,  and 
that  it  is  slight.  He  carries  his  opinion  so  far  as  to  assert  at 
the  same  place,  that  in  locomotives  the  water  mingled  with  the 
steam  coming  from  the  boiler  amounts  to  from  twenty-five  to 
thirty  per  cent  of  the  whole ;  that  being  the  percentage  re- 
quired to  make  the  adiabatk  curve  agree  with  the  actual  ex- 
pansion curve  of  the  indicator-card.  In  a  problem  he  assumes 
fifteen  per  cent  of  priming.  Again,  he  states  that  the  steam 
in  the  clearance  space  is  superheated  by  the  compression,  as  it 
would  be,  if  nearly  dry,  in  a  non-conducting  cylinder.  In  later 
writings  he  has  receded  in  part  from  this  position. 

Comparison  with  the  experimental  performance  of  engines 
shows  that  these  theories  are  frequently  in  error  by  a  large 
amount,  which  must  be  due  to  the  neglect  of  the  effect  of  radi- 
ation and  of  the  thermal  action  of  the  walls  of  the  cylinder. 
All  investigators  from  the  time  of  Watt  have  known  that  the 
omission  of  these  actions  involved  an  error,  and  their  failure  to 
include  them  in  their  theories  is  due,  in  most  part,  to  the  lack 
of  experimental  data.  The  theories  are  to  be  considered  as 
first  approximations,  without  which  the  existence  and  amount 
of  the  error  would  never  have  been  known  ;  and  the  complete 
theory  is  to  be  obtained  by  the  insertion  of  the  missing  quanti- 
ties in  the  old  theories,  which  with  this  exception  are  correct 
in  principle. 

At  the  present  time  such  a  complete  theory  cannot  be 
stated,  because  the  form  even  of  the  factors  depending  on  the 
thermal  action  of  the  walls  has  not  been  discovered,  and  all  at- 
tempts to  introduce  such  factors  have  led  to  unsatisfactory  re- 

*  Steam-engine  and  other  Prime  Movers,  p.  421. 
f  Mechanische  Warmetheorie,  pp.  421,  486,  499. 


THE   STEAM-ENGINE.  185 

suits.  The  proper  direction  of  investigation  appears  to  be  to 
determine  the  thermal  action  of  the  walls  quantitatively,  in  en- 
gines of  different  forms,  and  working  under  different  conditions, 
so  that  bad  construction  and  methods  of  working  may  be  avoid- 
ed, and  ultimately  a  complete  theory  may  be  constructed. 
Though  a  large  amount  of  experimental  information  exists,  the 
larger  part  cannot  be  used  for  this  purpose,  because  the  experi- 
ments, though  sufficient  for  the  purposes  sought  by  the  experi- 
menters, fail  to  give  certain  essential  data.  This,  together 
with  the  complexity  of  the  subject,  has  made  all  attempts 
to  complete  the  theory  unsatisfactory  up  to  the  present  time. 
"""  Hirn's  Analysis. — The  best  analysis  of  the  action  of  the 
steam  in  the  cylinder  of  an  engine  is  given  by  Hirn,*  and  the 
most  complete  experiments  have  been  made  in  accordance,  by 
his  direction  or  under  his  inspiration.  He  calls  the  old  form 
of  theories  generic  theories,  while  his  form  he  calls  the  practical 
theory.  His  method  cannot  be  considered  as  a  complete  the- 
ory, since  it  does  not  allow  us  to  predict  the  action  of  a  new 
form  of  engine.  It  does,  however,  enable  us  to  determine  the 
real  behavior  of  existing  engines. 

The  clearest  statement  of  Hirn's  theory  is  derived  from 
some  memoirs  by  Zeuner,  f  in  which  the  equations  are  de- 
duced by  the  ordinary  methods  of  thermodynamics,  in  better 
form  than  that  given  by  Hirn  himself.  The  memoirs  are 
written  in  criticism  of  Hirn's  methods  and  conclusions,  but  the 
equations  are  accepted  by  both  writers,  as 
in  fact  they  must  be,  whatever  the  conclu- 
sions from  their  application  may  be. 

Let  Fig.  46  represent  the  cylinder  of  a 
steam-engine    and    the    diagram    of    the 

actual  cycle  without  lead  of  admission  or  F          Tj 1 

release.    Let  the  weight  of  the  mixture  of  ' 
steam  and  water  admitted  per  stroke  be 


M,  of   which  the  part  MX  is   steam    and  FIG.  46. 

M(\—  x)  is  water.     The  condition  of  the  mixture    is   known 

*  Theorie  Mecanique  de  la  Chaleur,  Tome  II. 

f  Revue  universelle  des  Mines,  vol.  xi.  p.  15,  vol.  xiii.  p.  I. 


1  86  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

from  the  pressure  /,  with  which  it  enters  the  cylinder,  and 
from  x.  Let  the  volume  of  the  clearance  be  F0,  that  of  the 
piston  displacement  up  to  cut-off  be  V^  ;  let  the  total  piston  dis- 
placement be  F2  ,  and  the  volume  to  be  displaced  by  the  pis- 
ton between  compression  and  the  end  of  the  stroke  be  F8. 
Let/,,/,,/3,  and/0  be  the  pressures  at  cut-off,  at  the  end  of 
the  stroke,  at  compression,  and  at  admission,  while  the  .corre- 
sponding values  of  x  are  distinguished  by  the  same  subscripts. 
Finally,  let  the  weight  of  the  water  and  steam  in  the  clearance 
space  during  compression  be  M0. 

The  heaf  required  to  raise  M  units  of  weight  of  water  from 
freezing-point  to  the  temperature  t  corresponding  to/,  and  to 
evaporate  the  portion  MX,  is 


For  steam  superheated  to  the  temperature  tx, 

+  ff(tx-t)]  .....     (246) 


The  internal  heat  of  the  mixture  in  the  clearance  space  at 
admission  is 


At  cut-off  the  internal  heat  of  the  mixture  in  the  cylinder  is 


During  the  admission  the  external  work  done  is  Wa1  and 
the  walls  of  the  cylinder  have  absorbed  the  heat  Qa  ;  hence 

G  +  ^o(?o  +  *oP0)  =  AWa+Qa  +  (M+  M0)  fo  +  xlPl\     (247) 

In  case  the  steam  remains  superheated  up  to  the  point  of 
cut-off,  this  equation  cannot  be  used,  but  that  condition  does 
not  commonly  occur  in  practice.  As  the  heat  absorbed  by  the 
walls  is  given  a  positive  sign,  the  heat  yielded  should  have  the 
negative  sign  ;  but  it  is  more  convenient  to  give  the  positive 
sign  to  all,  and  then  in  calculation  of  a  problem  the  numerical 


THE   STEAM-ENGINE.  l8/ 

values  will  receive  the  proper  sign  to  signify  in  which  way  the 
heat  passes. 

The  internal  heat  of  the  mixture  in  the  cylinder  at  the  end 
of  expansion  is 

jflf-f  JQ^+f^, 

the  external  work  done  is  Wb,  and  the  heat  yielded  by  the 
walls  of  the  cylinder  is  Qb.  As  stated  above,  the  numerical 
value  of  Qb  when  heat  is  yielded  has  the  negative  sign  ;  if  heat 
is  given  to  the  walls  during  expansion,  which  may  occur  if  the 
steam  is  very  strongly  superheated,  the  numerical  value  is 
negative,  but  in  such  case  equation  (247)  cannot  be  used. 
Since  no  heat  comes  from  sources  outside  of  the  cylinder, 

(M+  Mt)  (q,  +  xlPl)  =  AW>  +  Q>+  (M  +M,)  \qt  +  x^.    (248) 

During  the  exhaust  the  work  Wc  is  done  by  the  engine  on 
the  steam,  and  the  walls  of  the  cylinder  yield  the  heat  Qc-t  the 
heat  carried  away  by  the  water  resulting  from  the  condensa- 
tion of  steam  in  the  condenser  is  Mq^  q^  being  the  heat  of  the 
liquid  corresponding  to  the  pressure  in  the  condenser  ;  the 
heat  carried  away  by  the  cooling  water  is  G(gk  —  gt)  ,  G  being 
the  pounds  of  cooling  water  per  stroke,  and  q{  and  qk  the  heats 
of  the  liquid  at  the  initial  and  final  temperatures  ;  the  internal 
heat  in  the  steam  caught  in  the  cylinder  at  compression  is 


ofe,  + 
Combining  these  equations,  we  have 

xzPJ  +  AWc 
=  Q<  +  Mq,  +  G(qk  -  q^  +  Mfa  +  ^ps).     (249) 

During  compression  the  work  done  on  the  steam  is  Wd,  and 
the  heat  transferred  to  or  from  the  walls  of  the  cylinder  is  Qd. 
The  intrinsic  energy  at  the  end  of  compression  is 


o).     (250) 


1  88  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  four  equations  (246)  to  (250)  enable  us  to  determine 
the  interchange  of  heat  during  each  operation  of  the  cycle, 
provided  that  a  sufficient  number  of  data  can  be  obtained 
experimentally.  The  indicator-card  furnishes  means  of  deter- 
mining the  work  done  by  or  on  the  steam  in  each  operation, 
and  also  gives  the  pressures  from  which  the  values  of.  q  and  p 
can  be  found.  The  weight  M  may  be  determined  by  weighing 
the  feed-water  or  else  the  condensed  steam,  when  a  surface 
condenser  is  used.  The  weight  of  cooling  water  must  be  de- 
termined by  direct  measurement;  also  the  temperature  /4,  tK, 
and  ti  must  be  observed  directly.  If  the  entering  steam  is 
moist,  x  must  be  determined  by  a  calorimeter  experiment  ;  if  it 
is  superheated,  tx  may  be  observed  by  a  thermometer  in  the 
steam-pipe  near  the  engine.  The  values  remaining  are  M0,  xQy 
xiy  x^y  and  xz  . 

The  specific  volume  of  a  mixture  of  steam  and  water  is 

v  •=.  xu  -f-  a  ; 

or,  since  the  volume  occupied  by  the  water  in  the  cylinder  is 
small  compared  with  that  occupied  by  the  steam, 

v  —  xu,     and     V  —  Mxu.    .     .     .     .     .     (251) 

If  desired,  the  exact  value  of  v  may  be  carried  into  the 
equations,  but  at  the  expense  of  a  complication  which  does  not 
seem  necessary  in  the  present  state  of  the  subject. 

From  equation  (251), 

9u9=  F0;  ..........     (252) 

.=  V.+  V.-t  .     .     .     .     .     ...     (253) 

u^r.+  r^    .....   (254) 

u,=  F0+^  ......     (255) 


Substituting  in  equations  (246)  to  (250),  and  solving,  for  the 
quantities  of  heat  interchanged  between  the  steam  and  the 
walls  of  the  cylinder,  we  have 


THE  STEAM-ENGINE.  189 


J  ~  -A  Wa;      (256) 

l 


;     (257) 


+  AW,;    (258) 

*3 

<.   .    .    .    (259) 

^3  **0 

In  these  last  four  equations  the  only  quantity  on  the  right- 
hand  side  which  is  not  determinable  by  direct  observation  is 
M0.  These  equations  assume  that  the  steam  is  always  in  equi- 
librium, or  that  the  energy  due  to  velocity,  eddies,  and  commo- 
tion is  inappreciable. 

To  determine  M9,  Hirn  makes  the  assumption  that  x^  is 
unity,  or  that  the  steam  is  dry  at  the  beginning  of  compression. 
In  some  other  experiments,  in  which  the  compression  is  small 
and  the  vacuum  good,  he  assumes  that  M9  is  so  small  that  it 
may  be  neglected.  The  first  assumption  is  one  commonly 
made,  and  the  second  cannot  cause  much  error  under  the  con- 
ditions given,  if  the  first  is  allowable.  Zeuner  points  out  that 
if  M0  is  taken  too  small,  the  equations  deduced  will  show  a 
much  greater  apparent  action  of  the  walls  than  really  occurs, 
and  he  states  that  the  assumption  of  a  sufficiently  large  value 
of  M9  ,  i.e.,  of  a  large  enough  amount  of  water  in  the  clearance, 
will  make  the  terms  Qa,  Qb,  Qc,  and  Qd  very  small. 

The  total  work  deduced  from  the  indicator  is 

W=  Wa+  Wb-  Wc-  Wd.     ....     (260) 

If  the  heat  lost  by  radiation  during  one  stroke  is  Qe  and 
that  furnished  by  condensation  of  steam  in  the  jacket  is  <2y, 
then 

(260 


190  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Adding  the  equations  (256)  to  (259),  member  to  member, 
and  using  equations  (261)  and  (260),  we  have 

Q,-Qj^Q-Mq^-G(qt-q>)-AW,.      .      (262) 

which  might  have  been  written  directly,  since  it  is  apparent 
that  if  we  subtract  from  the  heat  supplied  the  heat  rejected 
and  the  heat  changed  into  work,  the  remainder  is  the  heat  lost 
by  radiation.  When  the  heat  supplied  by  the  jacket  is  greater 
than  that  lost  by  radiation,  both  sides  of  equation  (262)  be- 
come negative.  Again,  Qj  is  zero  when  a  jacket  is  not  used. 

Equation  (262)  gives  a  method  of  calculating  the  heat  lost 
by  radiation,  a  quantity  which  can  be  determined  directly  only 
when  a  steam-jacket  is  used,  and  which  is  then  subject  to  un- 
certainty. It  is,  however,  to  be  remarked  that  the  equation 
(262)  determines  Qe  by  subtraction,  and  therefore  it  is  affected 
by  the  accumulated  error  of  the  experiment,  which  may  be  much 
larger  than  the  uncertainty  of  a  direct  determination  when  a 
jacket  is  used. 

If  Qe  and  Qj  are  determined  directly,  then  equation  (261)  is 
another  equation  of  condition,  so  that  by  its  aid  equations 
(251)  to  (259)  may  be  solved  for  M0 ;  or  what  is  more  conven- 
ient, the  equation  (262)  may  be  used  as  a  check  on  the  equa- 
tions for  determining  the  quantities  of  heat  Qa,  Qb,  Qc,  and 
Qd1  and  thus  the  assumption  made  in  determining  M0,  i.e.,  x^  — 
I,  may  be  tested. 

The  storing  of  the  heat  Qd  and  the  restoring  of  heat  Qc, 
both  at  a  varying  temperature,  are  productive  of  a  loss  of 
efficiency ;  but  the  most  serious  loss  is  due  to  the  direct  loss  of 
the  heat  Qct  which  is  thrown  into  the  condenser  without  com- 
pensation.  In  many  engines,  Qc  is  the  most  serious  cause  of 
low  efficiency;  it  is  frequently  several  times  as  large  as  all  the 
heat  changed  into  work.  Hirn  has  proposed  to  make  Qc  a 
measure  of  the  advantage  of  various  devices,  such  as  super- 
heating, steam-jackets,  compounding,  etc. 

The  equations  are  deduced  for  an  engine  having  a  surface 
condenser ;  for  one  having  a  jet  condenser,  q^  and  qk  become 
identical.  For  a  non-condensing  engine  equation  (258),  con- 


THE   STEAM-ENGINE.  IQI 

taining  quantities  depending  on  the  condenser,  cannot  be  used, 
but  by  aid  of  equation  (262)  those  quantities  may  be  elimi- 
nated, giving 


V,)      -  (  F0  + 

1*1  tta 

(263) 

which  may  be  used  for  a  non-condensing  engine,  provided  that 
Qc  and  Qj  are  both  determined  by  direct  observation. 

Hirn  has  used  both  equation  (258)  and  equation  (263)  for 
determining  Qc,  to  which  he  attaches  so  much  importance,  and 
thereby  obtains  a  check  on  his  work.  The  check  is,  of  course, 
equivalent  to  determining  Qe,  the  heat  of  radiation  by  equa- 
tion (262),  as  well  as  by  direct  observation.  Or  the  comparison 
of  results  by  the  two  methods  may  be  considered  to  show  the 
combined  error  of,  first,  the  observations,  and,  second,  the 
method  of  calculating  the  steam  caught  in  the  clearance  space. 
Hirn's  original  work  and  that  of  his  school  is  stated  in  the 
numerical  solution  of  special  problems  ;  consequently  the  real 
meaning  of  the  check  from  the  two  methods  of  calculation  is 
not  so  clearly  presented,  and  the  coincidence  of  results,  from 
apparently  independent  methods,  is  more  striking  than  in  the 
discussion  just  given. 

In  certain  very  important  experiments  by  Hirn  and  by 
Hallauer,  the  compression  was  nearly  if  not  quite  absent, 
which,  with  the  low  absolute  pressure  in  the  condenser,  made 
M0,  calculated  by  the  usual  method,  so  small,  that  it  was  neg- 
lected. This  reduced  equations  (258)  and  (263)  to 

(264) 
e).     (26s) 


The  result  by  equation  (264)  was  considered  to  be  the  direct 
result,  and  that  by  equation  (265)  the  proof  of  the  correctness 
and  accuracy  of  the  theory  and  experiment.  The  numerical 
calculation  involved  some  minor  differences  which  could  not 
seriously  affect  the  result.  When  the  amount  of  the  back 


I92 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


pressure,  or  of  the  compression,  forbade  the  use  of  these  equa- 
tions, a  method  nearly  equivalent  to  equations  (262)  and  (263) 
was  employed. 

PROBLEM. — The  following  are  the  data  of  a  test  made  on 
a  Harris-Corliss  engine  in  the  laboratory  of  the  Institute    of 
Technology,  together  with  the  calculation  of  the  results : 
Diameter  of  the  engine,       ....     8  inches 

Stroke, 2  feet 

Piston  displacement:  crank  end,.     .     0.6791  cu.  ft. 

head  end,    .     .     0.7016       " 
Clearance,  per  cent  of  piston  displacement : 

crank  end, 3.75 

head  end, 5.42 

Boiler-pressure  by  gauge,    ....     77.4  pounds 

Barometer,    .........     14.8        " 

Condition  of  steam,  one  per  cdnt  of  moisture. 
Events  of  the  stroke  : 

Cut-off :   crank  end, 0.306  of  stroke 

head  end, 0.320     " 

Release  at  end  of  stroke. 

Compression:    crank  end,    .     .     .     0.013  of  stroke 

head  end,      .     .     .     0.0391     " 
Duration  of  the  test,  one  hour. 
Total  number  of  revolutions,  .     .     .     3692 

Weight  of  steam  used, 548  pounds 

Weight  of  condensing  water  used,  .     14,568       " 
Temperatures : 

Condensed  steam, /4  =  141°.  I  F. 

Condensing  water :    cold,     .     .     .     t;  —    52°-9  ^. 
warm,  .     .     .     tk=    88°.3  F. 

ABSOLUTE    PRESSURES,    FROM    INDICATOR-DIAGRAMS,    AND 
CORRESPONDING    PROPERTIES   OF   SATURATED   STEAM. 


CRANK  END. 

HEAD  END. 

/ 

9 

p  -^ 

u 

/ 

g 

p 

u 

Cut-off 

83.6 

284.6 

813.0 

'    5-iQO 

83-3 

284.4 

813.2 

5.207 

Release  

29.2 

217.8 

864.8 

13-924 

3!-9 

222.9 

861.8 

12.804 

Compression.  . 
Admission  .... 

14.8 
21.8 

181.1 
201.5 

893-2 
877.4 

26  .  464 
18.344 

I4.8 
29.8 

181.1 
'219-0 

893.2 
863.9 

26.464 
13.664 

THE   STEAM-ENGINE. 


193 


MEAN    PRESSURES,    AND    HEAT    EQUIVALENTS   OF   EXTERNAL 

WORKS. 


CRAN 

K  END. 

HEAD 

END. 

Mean  Pressures. 

Equivalents  of 
Work. 

Mean  Pressures. 

Equivalents  of 
Work. 

87.7 

3-  36a 

80.3 

3.7II 

Expansion                •      .  . 

44      *? 

3.877 

47    I 

41  ^Q 

Exhaust              

14.8 

i   836 

14   8 

I    847 

Compression  

18.3 

O.O2QQ 

21.8 

o  1104 

VOLUMES,    CUBIC    FEET. 


CRANK  END. 

HEAD  END. 

At  cut-off             V 

r  -4-  V 

O.2333 

0.2626 

At  release,            V 

^0  +  F2  

o  .  7046 

o.  7396 

At  compression   V 

O  O343 

0,065^ 

At  admission, 

°^o 

O.O255O 

0.03806 

At  the  boiler-pressure,  92.1  pounds  absolute,  we  have 

r  —  888.4,  3  =  291.7. 

The  steam  used  per  stroke  is 


The  steam  caught  in  the  clearance  space  at  compression,  on 
the  ^assumption  that  the  steam  is  then  dry  and  saturated,  is 
obtained  by  multiplying  the  mean  volume  at  that  point  by  the 
weight  of  one  cubic  foot  of  steam  at  the  pressure  at  compres- 
sion ; 

0.0343+0.0655  I 

^F-     -x^^raoo2IPounds: 

M  -\-  M0  =  0.0742  +  0.0021  =  0.0763  pounds. 
The  condensing  water  used  per  stroke  is 
14568 

C  =  ^r36^=1-973- 

Q  =  M(xr  +  $)  =  0.0742(0.99  X  888.4  +  291.7)  =  86.903  ; 


194  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


,-(y,+  yi)       -AW, 

UQ  Hl 

=  86.903  +  O.O02I  X  i(201.5  -f-  219.0)  —  0.0763  X  284.5* 


I/  813.0   ,  8n.2\       3.369+3.711 

—  -  (0.2333  X  —  —  -f  0.2626  X  —  —  :    —         y     —  — 
21  5.19  5-207/  2 

=  86.903  +  0.441—21.707.+  1.815-38.778-3.540  =  25.134; 


,    (  222.0  +  2I7.8\ 

-0.763(284.5--       ££_      -J+  38.778 

i/  864.8  86i.8\       3.877+4.159 

--   0.7046  x  -       --  +  0.7396  x  - 

2  \  '      13-924  *        12.804^       2 

—  4.898  +  38.778  -  46.771  -  4.018  =  -  7.1  13  ; 


222.9  +  217.8 
=  0.0763  x  -  -—  -  -  -  —  0.0021  x  1  8  1.  1  +46.771 


=  16.809  —  0.380  +  46.77  —  1.684  —  8.1  10  —  69.644  +  1.841 
=  -14.397;  " 


=  0.0021 

0.0299  O.HO4 

2 

=  —  0.061  +  1.684  —  1.815+0.070—  —0.122; 

*=2$.  134-7.113-  14.397-0-122^3.502^  Qe. 


THE  STEAM-ENGINE.  195 

Also,  equation  (262)  for  this  case  gives 

Qe=Q-Mq>-G(qk-q^-AW  ^ 

=  86.903  —  8.  1  10  —  69.644  —  (3.735  +  3.846  —  1.841  —  0.070) 
=  86.903  —  8.1  10  —  5.647  =  3,502. 

It  is  to  'be  remembered  that  the  heat  lost  by  radiation  and 
conduction  per  stroke,  when  estimated  in  this  manner,  is 
affected  by  the  accumulated  errors  of  observation  and  compu- 
tation, which  may  be  a  large  part  of  the  total  value  of  Qe  as 
determined. 

Dropping  superfluous  significant  figures,  we  have  in  B.  T.  U. 

£  =  86.9,   <2a=24.9,    Qb  =  6.9,    <2c=i44,  &=—  0.12,  <2,=3-5- 
The  horse-power  of  the  engine  is 

778  X  5.670  x  3692  X  2 

-60^330^"  16.35  H.P., 

and  the  steam  per  horse-power  per  hour  is 


5  =  33-5  pounds. 

A  consideration  of  the  theory  just  elaborated  will  show  that 
the  true  condition  of  the  steam  at  compression  is  of  great  im- 
portance. Zeuner.  shows  that  for  some  of  Hallauer's  experi- 
ments an  assumption  that  M0  =  M  will  reduce  Qc  to  zero.  In 
reply  Hirn  shows  that  such  an  assumption  does  not  reduce  the 
other  quantities,  Qa  ,  Qb  ,  and  Qd  ,  to  zero,  as  ought  to  be  the 
case  if  there  is  no  interchange  of  heat  between  the  cylinder  and 
the  steam  ;  and  Hallauer  shows  that  the  behavior  of  the  steam 
during  compression  cannot  be  accounted  for  on  such  an  as- 
sumption. Again,  the  conditi6n  of  the  exhaust  steam  may  be 
calculated  in  some  experiments  by  considering  the  condenser 
to  be  a  calorimeter,  and  such  a  calculation  gave  about  six  per 
cent  of  water.  If  the  steam  in  the  cylinder  at  compression 
had  the  same  amount  of  water,  the  error  of  considering  it  dry 


196 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


would  be  small.  Moreover,  water  which  collects  in  the  cold 
cylinder  of  an  engine  when  started,  quickly  passes  away,  as  is 
indicated  by  the  change  of  the  sound  of  exhaust  from  dull  and 
heavy  to  dry  and  short.  All  this  shows  that  a  large  quantity 
of  water  in  the  clearance  space  is  improbable  if  not  impossible, 
but  it  does  not  entirely  justify  the  assumption  that  the  steam 
is  dry  at  compression.  Experiments  made  on  engines  having 
a  large  compression  may  give  light  on  the  subject. 

Surface  Condensers. — The  proper  discussion  of  condens- 
ers can  be  given  only  in  connection  with  the  theory  of  the 
steam-engine,  though  it  is  commonly  treated  as  a  separate 
problem. 

Let  Fig.  47  represent  the  cylinder  of  a  steam-engine  and  a 
surface  condenser.  The  piston  is  at  the  end  of  the  stroke,  and 

the  cylinder  contains  M  pounds  of  a 
mixture  of  steam  and  water,  having 
the  conditions  determined  by  /a  and 
x^.  The  cylinder  by  the  opening  of 
the  exhaust-valve  is  put  in  communi- 
cation with  surface  condenser  con- 
taining a  weight  M^  of  steam  and 
water,  having  the  condition  deter- 
mined by  £,  and  ^2.  We  may  im- 
agine the  process  to  be  divided  into 
two  parts:  (i)  the  steam  and  water 
in  the  cylinder  and  condenser  min- 
gle, and  are  reduced  to  the  temperature  /2 ;  (2)  the  piston 
passes  to  the  other  end  of  the  stroke  and  reduces  the  volume 
from  V,-\-  F2to  F2. 

The  result  would  be  the  same  if  we  imagine  the  steam  in 
the  cylinder  (i)  to  be  reduced  to  the  temperature  *a  before  the 
exhaust-valve  opens,  and  then  (2)  after  the  valve  opens  to  be 
reduced  from  the  volume  Vl  +  F2  to  F2 . 

In  the  first  process  the  steam  and  water  is  reduced,  at  con- 
stant volume,  from  the  temperature  ^  to  /2 .  To  find  the  heat 
abstracted,  we  have 

dQ  =  M.AdE  =  M^dq  +  d(xp)~\. 


FIG.  47. 


THE   STEAM-ENGINE.  197 

But  XtU,  -f-  o-  =  xu  +  o-  ; 


A  a  =  ^,  *,-*,+*, 

At  the  end  of  this  process  we  have  a  volume  Fi  -f-  F2  of 
steam  and  water  having  a  weight  Ml  -\-  Mt  =  M,  and  having  a 
value  xf  that  could  be  found  if  desired. 

The  second  process  reduces  the  volume  from  Vl  -\-  F2  to  F2  , 
and  the  value  of  x  changes  again  and  becomes  x^'.  The  heat 
abstracted  is 

Mr^-x-}.  .    .     .....     .     .     .     (267) 

The  volumes  before  and  after  compression  are 
Vl+V,  =  M(^u,  +  <7); 
V,  =  Jf  (*,"*,  +  a)  I 
so  that  the  change  of  volume  is 


But,  from  the  initial  condition, 
V,  =  M,(xlUl  +  a)  ; 
so  that,  if  cr  be  neglected, 

*•*• 


M=M, 


.    Substituting  this  in  equation  (267),  we  have  for  the  heat 
abstracted  during  the  second  process, 


+  A?  .....    (268) 

The  total  heat  withdrawn  during  both  processes  is,  there- 
fore, 

A*0]  ......     (269) 


198  THERMODYNAMICS  OF  THE   STEAM-ENGINE. 

But  during  the  exhaust  from  the  cylinder  of  an  engine  the 
walls  yield  to  the  steam  and  water  contained  the  heat  Qc,  and 
this  passes  into  the  condenser,  so  that  the  total  heat  to  be  car 
ried  away  by  the  cooling  water  is 

i)]-  •  •  •  (270) 


Each  unit  of  weight  of  cooling  water  in  passing  through  the 
condenser  will  acquire  qk—  qt  units  of  heat  ;  consequently  the 
pounds  of  cooling  water  for  one  pound  of  mixture  of  water  and 
steam  drawn  from  the  cylinder  will  be 


(271) 


If  it  be  assumed  that        =  o,  that  xl  =  i,  and  that  Ap^  is 
the  same  as  Ap^u^  ,  then  the  expression  becomes 


qk  — 


(272) 


The  expression  commonly  used  for  calculating  the  cooling 
water  required  is 


in  which  1  is  the  total  heat  of  steam  at  the  pressure  in  the  ex- 
haust pipe. 

The  expression  is  deduced  by  assuming  that  the  exhaust 
steam  is  dry  and  saturated,  and  that  it  is  condensed  and  cooled 
to  the  temperature  ^  by  the  cooling  water,  which  thereby  gains 
the  temperature  tk  —  t{  . 

Some  experiments  by  Hallauer*  on  a  condensing-engine 
using  saturated  and  superheated  steam,  show  that  the  exhaust 
steam  in  that  engine  contained  from  6  to  12  per  cent  of  mois- 
ture. Experiments  in  the  laboratory  of  the  Institute  of  Tech- 

*  Bulletin  de  la  Soc.  Ind.  de  Mulhouse,  vol.  xlvii.  1877. 


THE  STEAM-ENGINE.  199 

nology,  on  non-condensing  engines,  show  in  general  a  less 
amount  of  moisture  in  the  exhaust  steam.  It  may  be  concluded 
that  exhaust  steam  from  an  engine  is  seldom  or  never  super- 
heated, that  it  usually  contains  a  moderate  amount  of  moisture, 
and  that  it  is  sufficient  to  assume  it  to  be  dry  and  saturated, 
for  calculation  of  the  condensing  water  required. 

Cooling  Surface. — Experiments  on  the  quantity  of  cooling 
surface  required  by  a  surface-condenser  are  few  and  unsatisfac- 
tory, and  a  comparison  of  condensers  of  marine  engines  shows 
a  wide  diversity  of  practice.  Seaton*  says  that  with  an  initial 
temperature  of  60°,  and  with  120°  for  the  feed-water,  a  conden- 
sation of  13  pounds  of  steam  per  square  foot  per  hour  is  con- 
sidered fair  work.  A  new  condenser  in  good  condition  may 
condense  much  more  steam  per  square  foot  per  hour  than  this, 
but  allowance  must  be  made  for  fouling  and  clogging,  especially 
for  vessels  that  make  long  voyages. 

Seaton  also  gives  the  following  table  of  square  feet  of  cooling 
surface  per  indicated  horse-power : 

Absolute  terminal  pressure,  Square  feet 

pounds  per  sq.  in.  per  I.  H.  P. 

30  3 

20  2.5 

15  2.25 

I2|  2. 

10  1.8 

8  1.6 

6  1.5 

For  ships  stationed  in  the  tropics,  allow  20  per  cent  more ; 
for  ships  which  occasionally  visit  the  tropics,  allow  10  per  cent 
more ;  for  ships  constantly  in  a  cold  climate,  10  per  cent  less 
may  be  allowed. 

Jet  Condenser. — In  the  jet  condenser  the  cooling  water 
mingles  with  the  steam,  and  the  final  temperatures  of  both  be- 
come tk.  There  are  some  minor  differences  that  appear  in  the 
exact  expression  for  the  cooling  water  required  from  that  for 

*  Manual  of  Marine  Engineering. 


2OO  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

surface  condensers  ;  but  the  difference  is  slight,  and  in  any  case 
the  simple  expression 

*•  —  9k 


is  to  be  preferred  in  practice. 

The  capacity  of  a  jet  condenser  should  not  be  less  than  one 
fourth  of  that  of  the  cylinder  or  cylinders  exhausting  into  it, 
and  need  seldom  be  more  than  one  half.  One  third  of  the 
capacity  of  the  cylinder  or  cylinders  is  generally  sufficient. 

Designing  Engines.  —  The  only  question  that  is  properly 
discussed  here  is  the  probable  form  of  the  indicator-diagram, 
which  gives  immediately  the  method  of  finding  the  mean  effec- 
tive pressure  and,  consequently,  the  size  of  the  cylinder  of  the 
engine. 

The  most  reliable  way  of  finding  the  expected  mean  effec- 
tive pressure  in  the  design  of  a  new  engine  is  to  measure  an 
indicator-card  from  an  engine  of  the  same  or  similar  type  and 
size,  and  working  under  the  same  conditions. 

As  it  can  hardly  be  expected  that  a  diagram  of  exactly  the 
required  form  will  be  at  hand,  a  diagram  like  Fig.  48  may  be 
drawn,  using  the  proper  cut-off,  compression, 
and  clearance.  If  an  indicator-card  taken 
from  an  engine  under  similar  conditions  is 
attainable,  it  may  be  used  to  determine  ex- 
ponential equations  for  the  expansion  and 


compression  curves;  usually  the  exponent 
will  be  different  for  the  two  curves,  and  must  be  determined 
separately.  For  ordinary  work  it  is  sufficient  to  use  the  hyper- 
bola for  both  curves,  and  to  assume  the  steam  line  a  and  the 
back-pressure  line  c  to  be  parallel  to  the  atmospheric  line,  while 
the  lead  of  admission  and  exhaust  may  be  neglected.  It  is 
also  customary  to  assume  a  loss  of  pressure  of  one  or  two 
pounds  between  the  boiler  and  the  engine,  and  a  back  pressure 
of  a  like  or  greater  amount  above  the  pressure  in  the  condenser 
or  the  pressure  of  the  atmosphere,  as  the  case  may  be. 

If  the  diagram  is  drawn  to  scale,  the  area  and  mean  effec- 


THE   STEAM-ENGINE.  2OI 

live  pressure  may  be  found  by  measuring  it ;  or,  the  form  of 
the  expansion  and  compression  curves  being  assumed,  the  areas 
under  the  steam  line,  the  expansion  curve,  the  back-pressure 
line,  and  the  compression  curves  may  be  calculated  separately, 
integrating  between  limits  when  necessary,  and  therefrom  the 
resulting  area  of  the  diagram  and  the  mean  effective  pressure 
may  be  determined.  Ordinarily,  the  expansion  and  compres- 
sion curves  are  assumed  to  be  hyperbolae. 

Seaton*  gives  the  following  multipliers  for  finding  the  mean 
effective  pressure  from  that  calculated  by  the  process  described : 

MULTIPLIERS  FOR  FINDING  PROBABLE  M.  E.  P.,  SIMPLE  EXPANSIVE  ENGINE- 


(i)  Special  valve-gear,  or  with  separate  cut-off  valve, 
engine  jacketed  

O  Qd. 

(2)  Good  ordinary  valves,  large  ports,  engine  jacketed. 
(3)  Ordinary  valves  and  gears  as  in  general  practice, 
unjacketed  .        ..         .... 

o.  9-0.  92 
o  80—0  85 

To  estimate  the  consumption  of  steam,  we  may  calculate 
from  the  pressure  and  volume  at  release  the  weight  of  steam 
then  present  in  the  cylinder,  and  in  a  similar  manner  the 
weight  of  steam  caught  in  the  clearance  «space  from  the  volume 
and  pressure  at  compression,  both  under  the  assumption  that 
the  steam  is  dry  and  saturated.  The  difference  is  the  steam 
exhausted  per  stroke  under  the  assumption ;  but  to  get  a  fair 
estimate  of  the  probable  consumption,  it  is  necessary  to  add  a 
fraction  of  this  amount,  depending  on  the  style  and  size  of  the 
engine  and  on  the  conditions  under  which  it  is  to  run.  Suffi- 
cient data  for  this  purpose  seldom  exist ;  so  it  is  customary  to 
add  to  the  calculated  amount  one  fourth  to  one  third  of  itself, 
to  get  the  probable  consumption  of  non-condensing  engines  of 
medium  size. 

PROBLEM. — Required  the  dimensions  of  an  engine  to  give 
I oo  horse-power  ;  revolutions,  120;  gauge-pressure,  80  pounds; 
cut-off  at  ^  stroke  ;  release  at  end  of  stroke  ;  compression  at  -^ 
stroke,  and  clearance  5  per  cent. 

*  Manual  of  Marine  Engineering. 


202  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Assuming  hyperbolic  expansion  and  compression  gives  for 
the  mean  effective  pressure 


0.333  x  927  +  0-383  x  92-7  lo&         ~  l6  x  0.9 


—  0.15  X  1  6  log,  -   -  —  49.5  pounds, 

if  the  pressure  during   admission  is  78   pounds,  and   during 
exhaust  is  1.3  pounds  above  the  atmosphere. 

If,  further,  the  stroke  of  the  engine  is  twice  the  diameter, 
then 

2d 
x  —  X  120  x  2  x  49.5 


4         12 
ioo  =  — 


33000 
.*.   d  —  12.85,         s  —  25.70. 

The  volume  of  the  cylinder  will  be  1.93  cubic  feet,  and  the 
terminal  pressure  will  be  33.8  pounds  absolute.  At  33.8  pounds 
the  density  of  steam  is  0.08234,  and  at  16  pounds  it  is  0.04067. 
The  consumption  of  steam  per  horse-power  per  hour,  on  the 
assumption  of  dry  steam  at  release  and  compression,  will  be 

(0.08234X1.05— 0.04067X0. 1 5)  1.93  X2X  120X60 

-  =  22.3  pounds, 
ioo 

If  one  third  of  this  quantity  be  added,  then  the. estimated 
consumption  of  steam  will  be  30  pounds  per  horse-power  per 
hour. 

The  calculated  dimensions  are  stated  in  inches  and  hun- 
dreds, but  in  practice  the  engine  would  be  made  12$  inches  in 
diameter  by  25 J  inches  stroke  ;  or  possibly  the  dimensions  13 
by  25  would  be  chosen,  since  they  give  nearly  the  same 
volume. 


THE   STEAM-ENGINE. 


EXAMPLES. 

1.  Find  the  volume  of  the  cylinder  of  a  double-acting  steam 
engine  to  give  100  H.P.  at  60  revolutions  per  minute.     Assume 
it  to  run  on  Carnot's  cycle,  to  have  150  pounds  by  the  gauge, 
and  1.5  pounds  absolute  for  the  maximum  and  minimum  pres- 
sures, and  to  have  the  steam  dry  and  saturated  at  the  begin- 
ning of  the  adiabatic  expansion. 

2.  In  problem  i,  make  the  minimum  pressure  14.7  pounds. 

3.  Suppose  an  actual  steam-engine,  working   between  the 
same  pressures  as  in  Example  i,  to  use  18  pounds  of  steam  per 
hour,  and  to  run  without  compression.     Find  the  volume  of  the 
cylinder  if  the  steam  at  release  contains  20  per  cent  of  moisture. 

4.  Find  the  relative  sizes  of  cylinders  of  perfect  heat-engines 
using  water,  ether,  and  carbon  tetrachloride,  and  working  be- 
tween the  temperatures  of  100°  C.  and  10°  C. 

Suggestion  :  Find  the  work  of  Carnot's  cycle  for  one  kilo- 
gram ;  find  the  relative  weights  to  give  equal  quantities  of 
work,  and  thence  the  relatives  volumes. 

5.  Find  relative  sizes  in  Example  4  when  working  between 
the  pressures  of  5  atmospheres  and  -J-  of  one  atmosphere. 

6.  Make  calculations  for  Hirn's  analysis  for  the  experiments 
given  on  pages  305  and  334. 

7.  Find  the  weight  of  cooling  water  for  a  hundred  horse- 
power engine  using  20  pounds  pf  steam  per  horse-power  per 
hour,  the  vacuum  in  the  condenser  being  26  inches  of  mercury, 
the  temperature  of  the  condensed  water  being  120°  F.,  and  the 
temperatures  of  the  cooling  water  being  60°  F.  and  1  10°  F. 

8.  In  Example  7,  find  the  area  of  cooling  surface  for  a  sur- 
face condenser,  the  terminal  pressure  being  I2-J  pounds. 

9.  Calculate  the  problem  given  on  page  201,  assuming  as 
the  equation  of  the  expansion  curve 


=  const., 
and  for  the  compression  curve 

v™  —  const. 


CHAPTER   XIII. 

COMPOUND    ENGINES. 

IN  a  compound  engine,  steam  is  admitted  from  the  boiler 
into  a  small  cylinder,  from  which  it  is  exhausted  above  atmos- 
pheric pressure.  The  steam  is  then  admitted  to  a  large  cylin- 
der, from  which  it  passes  to  a  condenser.  If  we  assume  that 
the  steam  from  the  small  cylinder  is  exhausted  into  a  large 
receiver,  the  back  pressure  in  that  cylinder  and  the  pressure 
during  the  admission  to  the  large  cylinder  will  be  uniform.  If, 
further,  we  assume  that  there  is  no  clearance  in  either  cylin- 
der, that  the  back  pressure  in  the  small  cylinder  and  the  for- 
ward pressure  in  the  large  cylinder  are  the  same,  and  that  the 
expansion  in  the  small  cylinder  reduces  the  pressure  down  to 
the  back  pressure  in  that  cylinder,  the  diagram  for  the  small 
cylinder  will  be  ABCD,  Fig.  49,  and  for  the  large  cylinder 
DCEFG.  The  volume  in  the  large  cylinder  at  cut-off  is  equal 
to  the  total  volume  of  the  small  cylinder,  since  the  large  cylin- 
der takes  from  the  receiver  the  same  weight  of  steam  that  is 
exhausted  by  the  small  cylinder,  and,  in  this  case,  at  the  same 
pressure. 

The  case  just  discussed  is  one  extreme.  The  other  extreme 
occurs  when  the  small  cylinder  exhausts  directly  into  the  large 
cylinder  without  an  intermediate  receiver.  In  such  engines  the 
pistons  must  begin  and  end  their  strokes  together.  They  may 
both  act  on  the  beam  of  a  beam  engine,  or  they  may  act  on 
one  crank  or  on  two  cranks  at  180°  apart. 

For  such  an  engine,  ABCD,  Fig.  50,  is  the  diagram  for  the 
small  cylinder.  The  steam  line  and  expansion  line  AB  and  BC 

204 


COMPOUND  ENGINES. 


20$ 


are  like  those  of  a  simple  engine.  When  the  piston  of  the 
small  cylinder  begins  the  return  stroke,  communication  is 
opened  with  the  large  cylinder,  and  the  steam  passes  from  one 
to  the  other,  and  expands  to  the  amount  of  the  difference  of 
the  volume,  it  being  assumed  that  the  communication  remains 
open  to  the  end  of  the  stroke.  The  back-pressure  line  CD  for 


F  V 


FIG.  49. 


FIG.  50. 


the  small  cylinder,  and  the  admission  line  HI  for  the  large 
cylinder,  gradually  fall  on  account  of  this  expansion.  The  dia- 
gram for  the  large  cylinder  is  HIKG,  which  is  turned  toward 
the  left  for  convenience. 

To  combine  the  two  diagrams,  draw  the  line  abed,  parallel 
to  V'OV,  and  from  b  lay  off  bd  equal  to  ca  ;  then  d  is  one  point 
of  the  expansion  curve  of  the  combined  diagram.  The  point 
C  corresponds  with  H,  and  E,  corresponding  with  7,  is  as  far 
to  the  right  as  /  is  to  the  left. 

For  a  non-conducting  cylinder,  the  combined  diagram  for  a 
compound  engine,  whether  with  or  without  a  receiver,  is  the 
same  as  that  for  a  simple  engine,  which  has  a  cylinder  the 
same  size  as  the  large  cylinder  of  the  compound  engine,  and 
which  takes  at  each  stroke  the  same  volume  of  steam  as  the 
small  cylinder,  and  at  the  same  pressure.  The  only  advantage 
gained  by  the  addition  of  the  small  cylinder  to  such  an  engine 
is  a  more  even  distribution  of  work  during  the  stroke,  and  a 
smaller  initial  stress  on  the  crank-pin. 

Compound  engines  may  be  divided  into  two  classes — those 
with  a  receiver  and  those  without  a  receiver ;  the  latter  are 
called  "  Woolf  engines"  on  the  continent  of  Europe.  Engines 
without  a  receiver  must  have  the  pistons  begin  and  end  their 


206  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

strokes  at  the  same  time  ;  they  may  act  on  the  same  crank  or  on 
cranks  180°  apart.  The  pistons  of  a  receiver  compound  engine 
may  make  strokes  in  any  order.  A  form  of  receiver  compound 
engine  with  two  cylinders,  commonly  used  in  marine  work,  has 
the  cranks  at  90°  to  give  handiness  and  certainty  of  action. 
Large  marine  engines  have  been  made  with  one  small  cylinder 
and  two  large  or  low-pressure  cylinders,  both  of  which  draw 
steam  from  the  receiver  and  exhaust  to  the  condenser.  Such 
engines  usually  have  the  cranks  at  120°,  though  other  arrange- 
ments have  been  made. 

In  reality,  all  compound  engines  have  a  receiver,  or  a  space 
between  the  cylinders  corresponding  to  one,  and  in  no  case  is 
the  receiver  of  sufficient  size  to  entirely  prevent  fluctuation  of 
pressure.  In  the  later  marine  work  the  receiver  has  been  made 
small,  and  frequently  the  steam-chests  and  connecting  pipes 
have  been  allowed  to  fulfil  that  function.  This  contraction  of 
size  involves  greater  fluctuation  of  pressure,  but  for  other  rea- 
sons it  appears  to  be  favorable  to  economy. 

Compound   Engine  without   Receiver. — The   indicator- 
cards  from,  a  compound  engine  without  a  receiver  are  repre- 
sented by  Fig.  51.     The  steam  line  and  ex- 
pansion line  of  the  small  cylinder,  AB  and 
BC,  do  not  differ  from  those  of  a  simple 
engine.     At  C  the  exhaust  opens,  and  the 
steam  suddenly  expands  into  the  space  be- 
tween the   cylinders   and   the  clearance  of 
FlG- 5I-  the  large  cylinder,  and  the   pressure   falls 

from  C  to  D.  During  the  return  stroke,  the  volume  in  the 
large  cylinder  increases  more  rapidly  than  that  of  the  small 
cylinder  decreases,  so  that  the  back-pressure  line  DE  gradually 
falls,  as  does  also  the  admission  line  HI  of  the  large  cylinder, 
the  difference  between  these  two  lines  being  due  to  the  resist- 
ance to  the  flow  of  steam  from  one  to  the  other.  At  E  the 
communication  between  the  two  cylinders  is  closed  by  the  cut- 
off of  the  large  cylinder ;  the  steam  is  thus  compressed  in  the 
small  cylinder  and  the  space  between  the  two  cylinders  to  F, 
at  which  the  exhaust  of  the  small  cylinder  closes ;  and  the 


COMPOUND  ENGINES. 


2O7 


remainder  of  the  diagram  FGA  is  like  that  of  a  simple  engine. 
From  /,  the  point  of  cut-off  of  the  large  cylinder,  the  remain- 
der of  the  diagram  IKLMNH  is  like  the  same  part  of  the  dia- 
gram of  a  simple  engine. 

The  "  drop"  CD  at  the  end  of  the  stroke  of  the  small  cylin- 
der, and  the  difference  between  the  lines  DE  and  ///,  are  evi- 
dent losses  of  efficiency.  The  compression  EFG  for  the  small 
cylinder,  and  the  accompanying  independent  expansion  IK  in 
the  large  cylinder,  are  losses  of  power  in  the  engine  ;  but  the 
compression,  as  in .  a  simple  en- 
gine, fills  the  waste  spaces,  and 
in  this  case  mitigates  the  effect  of 
the  "  drop."  It  is  apparent  that 
there  would  be  a  loss  of  efficiency 
in  compounding  a  non-conducting 
engine,  yet  under  proper  circum- 
stances experiment  shows  an  ad- 
vantage in  compounding  engines 
with  metallic  cylinders. 

Fig.  52  is  a  diagram  taken  from 
a  compound  pumping-engine  at 
the  Lawrence,  Mass.,  water-works. 

Compound  Engine  with  Receiver. — In  the  receiver  com- 
pound engine  with  cranks  at  90°  the  cut-off  is  commonly  later 
than  half-stroke,  which  gives  rise  to  a  species 
of  double  admission.     The  diagrams  for  the 
small  and  large  cylinders  are  represented  by 
Fig.  53- 

When  the  exhaust  of  the  small   cylinder 
begins,  the  large  piston  is  at  about  half-stroke,  FlG-  53. 

and  communication  then  exists  through  the  receiver  between 
the  two  cylinders.  The  cut-off  of  the  large  cylinder  closes  this 
communication,  and  the  back  pressure  rises  in  the  small  cylin- 
der until,  at  about  half-stroke,  the  admission  to  the  other  end 
of  the  large  cylinder  makes  the  back  pressure  fall,  down  to  the 
compression  in  the  small  cylinder. 

The  admission  to  the  large  cylinder  begins  at  about  half- 


FIG.  52. 


208  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

stroke  of  the  small  piston,  with  a  free  communication  be- 
tween the  two  cylinders,  till  the  compression  begins  in  the 
small  cylinder.  The  steam  in  the  receiver  then  expands  with 
diminishing  pressure  to  about  half-stroke,  when  exhaust  at  the 
other  end  of  the  small  cylinder  begins,  causing  an  increase  of 
pressure  for  the  remainder  of  the  admission. 

Fig.  53#  gives  diagrams  from  the  high  and  low  pressure 
cylinders  of  a  receiver  compound  engine 
of  the  yacht  Gleam. 

The  diagrams  from  three  cylinder 
compound  engines,  and  from  other  ar- 
rangements, have  peculiarities  that  must 
be  investigated  separately  for  each  case. 
All  will  show  a  drop  at  the  end  of  the 
expansion  in  the  small  cylinder,  and  in 
general  a  loss  of  pressure  between  the 
small  and  large  cylinders. 

A  comparison  with  the  ideal  diagram,  Fig.  49,  will  show  a 
loss  of  efficiency  from  the  drop,  and  the  loss  of  pressure  be- 
tween the  small  and  large  cylinders,  and  yet,  as  with  the 
Woolf  engine,  compounding  under  proper  circumstances  is  art 
advantage. 

It  is  customary  to  attempt  the  comparison  of  the  expan- 
sion in  a  compound  engine  to  that  of  a  simple  engine  by  an 
adaptation  of  the  methods  of  Figs.  49  and  50,  making  allow- 
ance for  the  clearance  and  the  action  of  the  receiver  and  of 
the  compression.  More  or  less  complication  is  introduced  to 
meet  the  difficulties  arising,  yet  the  result  is  not  satisfactory. 
The  simplest  method,  which  applies  to  receiver  compound 
engines,  is  a  modification  of  Fig.  49.  The  diagrams  are  trans- 
ferred to  a  common  scale,  and  referred  to  the  same  axis  of 
pressure  and  volume,  each  being  set  off  to  the  right  of  the 
axis  OP  by  the  amount  of  its  own  clearance.  It  is  customary  to 
complete  the  process  by  drawing  a  rectangular  hyperbola  in  a 
manner  similar  to  that  used  for  a  simple  engine. 

The  whole  process  is  of  doubtful  utility,  the  more  espe- 
cially as  there  appears  to  be  no  reason  to  assume  the  hyperbola 


COMPOUND  ENGINES.  2OQ 

or  any  other  simple  curve  to  represent  the  actual  equivalent 
expansion  in  a  simple  engine.  The  several  gaps  that  appear 
in  such  a  combined  diagram,  due  to  drop,  loss  of  pressure  and 
compression,  seem  to  show  a  loss  as  compared  with  a  simple 
engine,  which  may  or  may  not  exist.  The  only  way  of  know- 
ing anything  about  the  performance  of  a  type  of  engine  is  to 
make  a  series  of  careful  tests  upon  it. 

Triple  and  Quadruple  Compound  Engines. — The  same 
influences  which  introduced  the  compound  engines,  when  the 
common  steam-pressure  changed  from  forty  to  eighty  pounds 
to  the  square  inch,  have  brought  in  the  successive  expansion 
through  three  cylinders,  the  high-pressure,  intermediate,  and 
low-pressure  cylinders,  now  that  125  to  170  pounds  pressure 
are  employed.  Just  as  three  or  more  cylinders  are  combined 
in  various  ways  for  compound  engines,  so  four,  five,  or  six  cylin- 
ders have  been  arranged  in  various  manners  for  triple  com- 
pound engines ;  for  example,  a  compound  engine  with  two 
cylinders  may  be  conveniently  changed  into  a  triple  compound 
engine  by  the  addition  of  a  small  high-pressure  cylinder  over 
each  of  the  existing  cylinders. 

Quadruple  engines  with  four  successive  expansions  have 
been  employed  with  high-pressure  steam,  but  with  the  advis- 
able pressures  for  present  use,  the  extra  complication  and  fric- 
tion make  it  a  doubtful  expedient. 

Horse-power  of  Compound  Engines.— For  the  first 
approximation  it  is  customary  to  calculate  the  horse-power  of 
a  compound  engine  of  any  sort,  as  if  the  total  expansion 
occurred  in  the  cylinder  or  cylinders  that  exhaust  into  the 
condenser;  and  it  is  assumed  that  the  expansion  curve  is  a 
rectangular  hyperbola. 

PROBLEM. — Let  the  boiler-pressure  be  80  pounds  by  the 
gauge,  or  94.7  pounds  absolute  ;  let  the  back  pressure  be  4 
pounds  absolute ;  and  let  the  total  number  of  expansions  be  six, 
so  that  the  volume  of  steam  exhausted  to  the  condenser  is  six 
times  the  volume  admitted  from  the  boiler.  Neglecting  the  effect 
of  clearance  and  compression,  the  mean  effective  pressure  is 

94-7  X  i  +  94.7  X  \  log,  f  -  4  x  i  =  40.06  =  M.E.P. 


210  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

\ 

If  the  large  cylinder  is  30  inches  in  diameter,  and  the  stroke 
is  4  feet,  the  horse-power  at  60  revolutions  per  minute  is 

7T3O8 

—  —  X  40.06  x  2  x  4  X  60  H-  33000  =  412  H.P. 

« 

Point  of  Cut-off.  —  Let  the  ratio  of  the  volumes  of  the  high 
and  low  pressure  cylinders  of  a  compound  engine  be  R,  let  the 
number  of  expansions  in  the  small  cylinder  be  e,  and  let  the 
total  number  of  expansions  be  E  ;  then 


(273) 

(274) 


PROBLEM.:  —  Let  the  ratio  of  the  cylinders  of  the  engine  dis- 

cussed in  the  preceding  paragraph  be  3  ;  with  the  same  stroke 

the  diameters  will  be  I7T5F  and  30  inches.     The  number  of  ex- 

'pansions  in  the  small  cylinder  will  be  f,  and  the  cut-off  for  that 

cylinder  will  be  at  ^  of  the  stroke. 

The  cut-off  in  the  large  cylinder  has  an  effect  on  the  distri- 
bution of  the  work  and  the  adjustment  of  the  maximum  pres- 
sure on  each  piston,  but  it  does  not  affect  the  preliminary  cal- 
culation of  mean  effective  pressure  and  horse-power. 

Ratio  of  Cylinders.  —  In  designing  compound  engines, 
more  especially  for  marine  work,  it  is  deemed  important  for 
the  smooth  action  of  the  engine  that  the  total  work  shall  be 
evenly  distributed  upon  the  several  cranks  of  the  engines,  and 
that  the  maximum  pressure  on  each  of  the  cranks  shall  be  the 
same,  and  shall  not  be  excessive.  In  case  two  or  more  pistons 
act  on  one  crank,  the  total  work  and  the  resultant  pressure  on 
those  pistons  are  to  be  considered  ;  but  'more  commonly  each 
piston  acts  on  a  separate  crank,  and  then  the  work  and  pressure 
on  the  several  pistons  are  to  be  considered. 

If  it  is  desired  that  the  work  shall  be  equally  divided  be- 
tween the  two  cylinders  of  a  receiver  compound  engine,  the 
ratio  of  their  volumes  may  be  found  as  follows.  Let  the  initial 
pressure  be/,  the  receiver  pressure/,,  and  the  pressure  in  the 


COMPOUND  ENGINES.  211 

condenser  zero ;  then,  on  the  assumption  that  the  volumes  are 

inversely  as  the  pressures, 

2? 

/=^A=^A-  "r    V  X.'     '     '     (2?$) 

Let  v  be  the  volume  of  the  small  cylinder  and  Fthat  of  the 
large  cylinder ;  then  the  works  done  in  them  may  be  assumed 
to  be 

v  V 

r  e)  —  vpl     and      -=  A( 


V 

Equating  these  quantities  and  substituting  v  for  -5  , 


Again,  substituting  for  e  and  /  from  equations  (274)  and 
(275),  and  reducing, 


logIO£-  0.4343 

-  .....     (276) 


If  it  is  desired  to  make  the  maximum  pressure  on  the  pis- 
tons the  same,  then  we  should  have 


(277) 


a  and  A  being  the  areas  of  the  small  and  large  pistons  respec- 
tively. If  the  stroke  is  the  same  for  the  two  pistons,  then  the 
volumes  are  proportional  to  the  areas,  so  that  equation  (277) 
becomes 

pv  =  p,V; 

V 
or,  substituting  for/  from  equation  (275),  and  for  —  its  value  E, 

R*=E  .........     (278) 

Applied  to  the  problem  stated  above,  the  ratio  of  the  vol- 


212  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

umes  of  the  cylinders  for  six  expansions  is  2.49  by  equation 
(276)  and  2.45  by  equation  (278). 

The  method  of  equation  (276)  assumes  that  there  is  no  drop 
to  the  receiver ;  a  larger  ratio  will  be  accompanied  by  a  drop, 
and  a  smaller  ratio  will  cause  the  steam  in  the  small  cylinder 
to  be  expanded  to  a  lower  pressure  than  that  in  the  receiver. 

In  practice  both  the  ratio  of  the  cylinders  and  the  total 
expansions  are  assumed,  and  then  the  distribution  of  work  and 
the  maximum  loads  on  the  crank-pins  are  calculated,  allowing 
for  clearance  and  compression.  Designers  of  engines  usually 
have  a  sufficient  number  of  good  examples  at  hand  to  enable 
them  to  assume  these  data.  In  default  of  such  data  it  may  be 
necessary  to  assume  proportions,  to  make  preliminary  calcula- 
tions, and  to  revise  the  proportions  till  satisfactory  results  are 
obtained.  For  compound  engines  using  80  pounds  of  steam 
pressure,  the  ratio  is  1:3  or  1:4.  For  triple  expansion  en- 
gines the  cylinders  may  be  made  to  increase  in  the  ratio  I  :  2 
or  i  :  2£. 

Calculations  for  Compound  Engines. — Instead  of  de- 
ducing equations  for  the  calculations  for  compound  engines,  a 
few  problems  will  be  solved  to  exhibit  the  method. 

EXAMPLE  I. — Boiler-pressure  80  pounds  by  the  gauge,  re- 
ceiver-pressure 1 8  pounds,  pressure  in  the  condenser  4  pounds 
absolute.  Ratio  of  the  cylinders,  3  ;  total  expansion,  6.  Clear- 
ance, 10  per  cent  for  the  small  cylinder  and  8  per  cent  for  the 
large  cylinder.  Compression  at  0.15  of  the  stroke  for  each 
cylinder. 

First  Solution. — An  approximate  solution,  neglecting  clear- 
ance and  compression,  will  first  be  made. 

The  cut-off  in  the  small  cylinder  will  be  at 

|  —  £  stroke. 

The  terminal  pressure  in  the  small  cylinder,  on  the  assumption 
of  hyperbolic  expansion,  will  be 

—  =  47.35  pounds  absolute. 


COMPOUND  ENGINES.  21$ 

The  drop  to  the  receiver  will  be 

47-35  -  (iS  +  H-7)  =  17-65  pounds. 

The  cut-off  in  the  large  cylinder  is  determined  by  the  con- 
dition that  it  must  draw  the  same  weight  of  steam  per  stroke 
from  the  receiver  as  is  delivered  to  it  by  the  small  cylinder. 
The  volume  v  is  discharged  by  the  small  cylinder  per  stroke, 
which  may  be  assumed  to  expand  to  the  volume 


29.7 

in  the  receiver  on  account  of  the  drop.     The  cut-off  in  the 
large  cylinder  is  therefore  at 


=  o   O    of  the  stroke> 


29.7  29.7  X  3 

The  mean  effective  pressure  in  the  small  cylinder  is 

94.7  X  JO  +  lo&  2)  -  29-7  =  5047. 
The  mean  effective  pressure  in  the  large  cylinder  is 

29.7  X  0.509  (i  +  log,  ^-i^j  -  4  =  20.03  pounds. 
The  mean  effective  pressure  reduced  to  the  large  cylinder  is 
—  +  20.03  =  36.85  pounds. 

This  result  may  be  compared  with  the  result  obtained  on 
page  209,  on  the  assumption  that  all  the  work  was  done  in  the 
large  cylinder,  i.e.,  40.06  pounds. 

The  division  of  work  between  the  two  cylinders  is  in  the 
ratio 

50.47  i 


3  X  20,03 


214  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  drop  to  the  receiver  might  be  reduced  by  shortening 
the  cut-off  of  the  large  cylinder,  but  such  an  arrangement 
would  produce  a  greater  inequality  in  the  distribution  of  work. 
On  the  other  hand,  the  work  will  be  more  equally  distributed 
with  a  longer  cut-off  on  the  large  cylinder,  but  that  would  give 
a  larger  drop  and  a  more  wasteful  engine. 

The  maximum  pressure  on  the  small  piston  is 

94.7  —  29.7  =  65.0  pounds, 
equivalent  to 

65.0 

=  21.7  pounds 

on  the  large  piston. 

The  maximum  pressure  on  the  large  piston  is 

29.7  —  4  =  25.3  pounds. 

Lengthening  the  cut-off  of  the  large  cylinder  will  increase 
the  pressure  on  the  small  piston  and  diminish  that  on  the 
large  piston. 

Second  Solution. — A  more  complete  solution  with  slightly 
different  results  can  be  given,  taking  account  of  clearance  and 
compression. 

The  cut-off  in  the  small  cylinder  will  be  taken  at  one-half 
stroke,  as  before. 

The  terminal  pressure  is 

-—- ' —  =  51.66  pounds  absolute. 

1. 10 

The  drop  to  the  receiver  is 

51.66  —  29.7  —  21.96  pounds. 
The  cut-off  for  the  large  cylinder  is  at 

— — =  0.5798  of  the  stroke. 

29-7  X  3          b/y 


COMPOUND  ENGINES.  21$ 

The  mean  effective  pressure  in  the  small  cylinder  is 

94.7  X  i  +  94-7  X  0.6  log.^g  -  29.7  X  0.85 

—  29.7  x  0.25  log,—  -  =  53.65  pounds, 


The  mean  effective  pressure  in  the  large  cylinder  is 

i.  08 
29.7  X  0.5798  -f  29.7  X  0.6598  log,       —    -  4  X  0.85 


-  4  X  0.23  log,          =  22.51  pounds. 

The  mean  effective  pressure  reduced  to  the  large  cylinder  is 
-  +  22.5  1  =  40.39  pounds. 

The  division  of  work  between  the  two  cylinders  is  in  the 
ratio 

53^5      =     i 
3  x  22.51       1.26* 

The  maximum  pressures  on  the  small  and  large  pistons  are 
the  same  as  calculated  before. 

EXAMPLE  2.  —  Let  the  data  of  Example  i  be  taken  for  a 
non-receiver  compound  engine.  For  such  an  engine  the  only 
effect  of  the  cut-off  on  the  large  cylinder  is  to  produce  a  com- 
pression in  the  small  cylinder  and  the  space  between  the  two 
cylinders  corresponding  to  the  receiver  of  a  receiver  engine. 
Let  the  cut-off  on  the  large  cylinder  occur  at  0.70  of  the  stroke. 
Let  the  volume  of  the  intermediate  space  be  o.io  of  the  dis 
placement  of  the  large  cylinder,  or  0.30  of  the  volume  of  the 
small  cylinder. 

The  terminal  pressure  in  the  small  cylinder,  as  in  the  second 
solution  of  Example  I.  is  51.66  pounds  absolute. 


2l6  THERMODYNAMICS  OF   THE   STEAM-ENGINE, 

When  the  exhaust-valve  opens,  the  steam  from  the  small 
cylinder  mingles  with  that  in  the  intermediate  space  and  in  the 
clearance  space  of  the  large  cylinder,  and  a  drop  occurs.  The 
steam  caught  by  the  compression  in  the  clearance  of  the  large 
cylinder  has  so  small  a  density  that  it  may  be  neglected.  The 
effect  of  the  steam  in  the  intermediate  space  may  be  esti- 
mated in  the  following  manner.  Disregarding  the  steam  in 
the  intermediate  space,  the  volume  \.\QV  of  steam  at  the  ter- 
minal pressure  51.66  may  be  assumed  to  occupy  the  volume 

(0.3  +  o.i)z/  +  o.i  F  +  (0.7  +  0.08)  V  —  3.042; 

at  the  cut-off  of  the  large  cylinder,  and  the  corresponding  pres- 
sure is 

51.66  x  i.i 

-  —  18.7  pounds. 
3-°4 

After  the  cut-off  occurs  the  steam  in  the  small  cylinder  at 
this  pressure  is  compressed  from  the  volume 

(0.3  +  o.  i)v  +  o.  i  V  —  0.77', 
which  it  then  occupies,  to  the  volume 

o.i  V '-f-  o.iv  —  0.4^, 
and  the  final  pressure  will  be 

18.71  x  —  =  32.7  pounds. 
0.4 

The  pressure  in  both  cylinders  after  the  drop  has  occurred 
may  be  assumed  to  be 

32.7  x  o.i  F+ 51.66  x  i.iv      66.64 

— r— n ^VTT —  =  — z-1  —  4°-6  pounds. 

i.i^  +  (o.i  +o.o8)F  1.64 

The  drop  is 

51.66  —  40.6=  1 1. 1  pounds. 


COMPOUND  ENGINES.  2 1/ 

The    corrected    pressure    at    cut-off   of  the    large    cylinder 
will  be 

66.64 


3-04 


=  21.9  pounds, 


instead  of  18.7  pounds  given  above,  and  it  appears  unnecessary 
to  make  a  second  approximation. 

The  mean  forward  pressure  on  the  small  piston  is 

94.7  x  i  +94-7  X  0.6  log,  —:  =  85.7  pounds. 

The  back  pressure  on  the  small  piston  and  the  forward 
pressure  on  the  large  piston  up  to  the  cut-off  of  the  large 
cylinder  is 

3-°4 
40.6  x  1.64^  loge  — g-  -T-  o.7(F—  v)  =  29.4  pounds. 

The  back  pressure  on  the  small  piston  from  the  cut-off  of 
the  large  cylinder  to  the  end  of  the  stroke  is  properly  divided 
into  two  parts,  the  first  part  ending  at  the  compression  of  the 
small  cylinder,  during  which  steam  is  compressed  in  the  small 
cylinder  and  its  clearance  and  the  intermediate  space,  and  the 
second  part  from  the  compression  to  the  end  of  the  stroke, 
during  which  steam  is  compressed  in  the  small  cylinder  and  its 
clearance  only.  For  our  present  purpose  it  is  sufficient  to 
make  the  calculation  on  the  assumption  that  the  compression 
of  the  small  cylinder  is  at  the  end  of  the  stroke,  which  gives 
for  the  back  pressure  of  this  part  of  the  stroke  of  the  small 
piston 

21.9  x  0.7^  log,,  —  -r-  0.3^  =  28.6  pounds. 
0.4 

The  mean  back  pressure  on  the  small  piston  is  therefore 
0.7  x  29.4  +  0.3  x  28.6  =  28.2  pounds. 


218  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

The  mean  effective  pressure  on  the  small  piston  is 
85.7  —  28.2  =  47.5  pounds. 

The  forward  pressure  on  the  large  piston  from  cut-off  to  the 
end  of  the  stroke  is 

21.9  x  0.78  log,  -  '-  -r-  0.3  =  18.5  pounds, 
o./o 

The  mean  forward  pressure  on  the  large  piston  is 

29.4  X  0.7  -|-  18.5  X  0.3  =  26.1  pounds. 
The  mean  back  pressure  on  the  large  piston  is 

4  X  0.85  +  4  X  0.23  log,  ££§=4-1  pounds, 

and  the  mean  effective  pressure  on  the  same  is 

26.1  —4.1  =  22  pounds. 
The  mean  effective  pressure  reduced  to  the  large  cylinder  is 

47  5 

r"  +  22  =  37.8  pounds. 

0 

The  division  of  work  between  the  two  cylinders  is  in  the 
ratio 

47-3    =   i 

3  X  22         1.4* 

The  maximum  pressure  on  the  small  piston  occurs  at  0.3  of 
the  stroke  when  the  back  pressure  is  a  minimum,  and  is  then 

94.7-21.9  =  72.8, 
which  is  equivalent  to  a  pressure  on  the  large  piston  of 

72.8 

=  24.3  pounds. 


COMPOUND  ENGINES.  219 

The  maximum  pressure  on  the  large  piston  is  about  35 
pounds. 

If  the  two  pistons  are  fixed  to  one  rod,  the  maximum  pres- 
sure, reduced  to  the  large  piston,  is  about  60  pounds.  The 
maximum  pressure  on  the  piston  of  a  simple  engine  using  the 
same  steam-pressure  and  expanding  the  same  number  of  times 
will  be  90.7  pounds  per  square  inch. 

The  drop  may  be  made  smaller,  or  if  desired  it  may  be 
made  to  disappear,  by  shortening  the  cut-off  of  the  large  cylin- 
der, and  experiments  show  that  a  gain  of  efficiency  accompa- 
nies such  a  change. 

EXAMPLE  3. — If  the  engine  were  made  with  a  receiver  and 
with  two  low-pressure  cylinders,  each  with  its  own  crank,  the 
drop  could  be  avoided,  and  a  good  distribution  of  the  work 
among  the  three  cylinders  could  be  attained.  The  clearance 
and  compression  will  be  neglected  in  this  solution. 

The  terminal  pressure  in  the  small  cylinder,  as  in  the  first 
solution  of  Example  I,  is  47.35  pounds  absolute,  and  this  is 
also  the  back  pressure  in  that  cylinder. 

The  mean  effective  pressure  in  the  small  cylinder  is 

94.7  X  J(i  +  log, 2)  —  47.35  =  42.82  pounds. 

To  compare  this  with  one  of  the  low-pressure  cylinders  this 
result  may  be  divided  by  f,  giving  28.55  pounds. 

The  cut-off  of  each  of  the  low-pressure  cylinders  must  be  at 
•J-  stroke. 

The  mean  effective  pressure  in  each  of  the  low-pressure 
cylinders  is 

47-35  X  \(\  +  log,  3)  -  4  =  25.79  pounds. 

There  is  no  drop,  and  the  equivalent  mean  effective 
pressure  reduced  to  one  low-pressure  cylinder  is 

A  ?  R  7 

— '- 1-  25.79  —  40.06  pounds, 

0 

as  found  on  page  209. 


22O  THERMODYNAMICS  OF   THE  STEAM-ENGINE. 

EXAMPLE  4.  —  A  triple-expansion  engine  using  steam  at  1  50 
pounds  gauge-pressure  has  the  volumes  of  the  cylinders  in  the 
ratio  I  :  2|-  :  6£  ;  and  the  cut-off  is  at  0.6  of  the  stroke  on  the 
high-pressure  and  intermediate  cylinder  and  at  0.75  of  the 
stroke  on  the  low-pressure  cylinder. 

Neglecting  the  effects  of  clearance  and  compression,  the 
total  expansion  is 


the  pressure  in  the  first  intermediate  receiver  is 

'•       ;-,      V^1^^6^  pounds;    '  • 

and  the  pressure  in  the  second  intermediate  receiver  is 

164.7  X  0.6 

—  ~  —  2  —  =  21.08  pounds  ; 

0.75  X  6.25 

while  the  pressure  in  the  condenser  may  be  taken  at  4  pounds 
absolute. 

The  mean  effective  pressure  in  the  high-pressure  cylinder  is 

164.7  X  o.6f  i  +  log,  ^J  -  65.88  =  83.41  pounds. 
The  mean  effective  pressure  in  the  intermediate  cylinder  is 

65.88  X  0.6(1  -f-  log*  —  g)  —  21.08  =  38.64  pounds. 
The  mean  effective  pressure  in  the  low-pressure  cylinder  is 
21.08  X  0.75(1  +  log,  -j  —  4  =  16.36  pounds. 


COMPOUND  ENGINES.  221 

The  distribution  of  work  among  the  three  cylinders  is  in 
the  proportion 


The  pressures  on  the  crank-pins  are  in  the  proportion 

164.7-65.88     65.88  —  21.08 
^fes  -^T     ~  =  21.08  -4::  1:1-14:  1-08. 

The  drop  to  the  first  intermediate  receiver  is 
164.7  x  O.6  —  65.88  =  32.94  pounds. 

The  drop  to  the  second  intermediate  receiver  is 
65.88  x  0.6  —  21.08  =  12.45  pounds. 

On  account  of  the  loss  of  pressure  between  the  boiler  and 
the  engine,  and  between  the  engine  and  the  condenser,  and  of 
the  resistance  of  valves  and  passages,  the  mean  effective  pres- 
sure calculated  as  in  the  preceding  examples,  taking  account 
of  clearance  and  compression,  is  not  realized  in  practice.  The 
following  table  of  multipliers  is  given  by  Seaton  *  for  finding 
the  probable  mean  effective  pressure  of  compound  marine  en- 
gines : 

MULTIPLIERS   FOR  FINDING   PROBABLE   M.E.P.     COMPOUND 

ENGINES. 


(1)  Expansion-valve  to  H.P.  cylinder,  large  ports,  cylinders  jacketed. 

(2)  Ordinary  slide-valves,  good  ports,  cylinders  jacketed 

(3)  General  practice  of  merchant  service,  early  cut-off  in  both  cylin- 


ders, without  expansion-valves  or  jackets. 


(4)  Fast-running  engines  of   type  and  design  usually  fitted    in  war 


ships. 


o . 9-0 . 92 
0.8-0.85 


0.7-0. 


o . 6-0 . J 


To  find  the  probable  mean  effective  pressure,  by  aid  of  this 
table,  the  mean  effective  pressure  for  each  cylinder  is  to  be  calcu- 
lated separately,  allowing  for  clearance  and  compression,  and  the 
result  multiplied  by  the  proper  factor.  Or  the  equivalent  mean 

*  Manual  of  Marine  Engineering. 


222  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

effective  pressure,  as  calculated  in  the  examples,  allowing  for 
clearance  and  compression,  may  be  multiplied  by  the  factor. 

A  fair  approximation  to  the  probable  mean  effective  pres- 
sure of  marine  engines  of  the  ordinary  type  can  be  obtained  by 
calculating  the  mean  effective  pressure  approximately,  on  the 
assumption  that  the  total  expansion  takes  place  in  one  cylin- 
der, not  allowing  for  clearance  and  compression,  and  then  mul- 
tiplying successively  by  0.96  and  by  the  proper  factor  from  the 
table. 

Hirn's  Analysis. — Since  the  admission  to  the  high-pres- 
sure cylinder  and  the  exhaust  from  the  low-pressure  cylinder  of 
a  compound  engine  do  not  differ  from  the  corresponding  parts 
of  the  cycle  of  a  simple  engine,  we  may  apply  the  equations 
deduced  for  the  simple  engine  to  the  determination  of  the 
value  of  Qc,  the  heat  rejected  from  the  walls  of  the  cylinder  to 
the  condenser. 

Hirn  and  Hallauer,  in  all  of  their  work,  content  themselves 
with  determining  explicitly  this  one  of  the  four  quantities,  Qa, 
Qb>  QC-,  and  Qd,  but  there  appears  to  be  no  reason  why  the 
other  three  should  not  be  determined  also,  for  compound  en- 
gines as  well  as  for  simple  engines,  provided  a  clear  idea  is 
obtained  of  their  meanings.  Qa  is  the  heat  absorbed  by  the 
walls  of  the  high-pressure  cylinder  during  the  admission  of 
steam  to  it ;  Qc  is  the  heat  rejected  to  the  condenser  by  the 
walls  of  the  low-pressure  cylinder  during  its  exhaust ;  and  Qd 
is  the  interchange  of  heat  during  the  compression  in  the  large 
cylinder.  Qb  appears  as  the  heat  yielded  by  the  walls  of  the 
cylinders  during  expansion,  but  it  is  an  incomplete  expression 
for  a  complicated  operation.  During  the  expansion  in  the 
small  cylinder  heat  is  yielded  by  its  walls  to  the  mixture  of 
water  and  steam ;  also  during  the  exhaust  heat  is  yielded  by 
the  walls  of  the  small  cylinder,  so  that  nearly  if  not  all  the 
water  present  is  vaporized  as  during  the  exhaust  of  a  simple 
engine.  In  the  large  cylinder  the  steam  is  condensed  on  the 
walls  during  the  first  part  of  the  admission  for  a  Woolf  engine, 
and  probably  up  to  cut-off  for  a  receiver  compound  engine,  and 
heat  is  consequently  absorbed  by  the  walls  of  that  cylinder, 


COMPOUND  ENGINES.  22$ 

but  that  heat  is  given  up  in  large  part  during  the  expansion  in 
the  remainder  of  the  stroke.  The  final  result  is  a  yielding  of 
heat  to  the  mixture  in  the  cylinder.  In  good  types  of  com- 
pound engines  the  value  of  Qc  is  small,  though  there  may  be  a 
large  interchange  of  heat  during  the  earlier  operations,  and 
this  fact  is  the  probable  explanation  of  the  good  efficiency  of 
such  engines. 

Of  the  four  quantities  of  work  found  in  the  equations  for 
finding  the  interchange  of  heat,  Wa  is  the  absolute  work  dur- 
ing admission  to  the  small  cylinder,  Wc  is  the  negative  work  of 
the  back  pressure,  and  Wd  the  negative  work  of  the  compres- 
sion for  the  large  cylinder.  Wb  is  the  total  work  of  expansion 
which  may  be  obtained  by  the  expression 

w=  wa+wt  +  wc+wd. 

Hallauer  does  not  state  clearly  how  Wb  is  obtained  in  the 
work  which  he  gives  for  compound  engines. 

The  following  method  is  proposed  as  an  extension  of 
Hirn's  theory  to  compound  engines,  with  the  hope  that  by  its 
aid  the  transfer  of  heat  from  the  walls  of  the  small  cylinder  to 
the  walls  of  the  large  cylinder,  with  kindred  phenomena,  may 
be  calculated  after  proper  experiments  are  made. 

The  method  can  be  applied  when  each  cylinder  has  its  own 
jacket  writh  separate  drain,  so  that  the  condensation  in  each 
and  the  radiation  from  each  can  be  determined  separately,  and 
when,  further,  all  the  data  from  the  condenser  can  be  obtained. 
For  the  high-pressure  cylinder,  as  for  a  non-condensing  simple 
engine,  we  have 


V,      -(V,+  V-AW.    (273) 

**o  **i 

,)-AWk.    (274) 


t  .....    (276) 


224  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

For  the  low-pressure  cylinder  the  heat  received  during 
admission,  Q't  cannot  be  obtained  directly,  but  it  can  be  ob- 
tained by  aid  of  equation  (264),  which  may  be  written 


Q=  Qe'~  Q/+M?;+  <%«'-?/)  +A  W  ;      .    .    .  •  .    .    (277) 
and  the  four  required  equations  may  be  written 


(278) 


-AWS;  .    (279) 


f-f+AWe';  .    (280) 


d'.      .    '.    (281) 

**3  **« 

With  triple  and  quadruple  expansion  engines  the  following 
method  may  be  used.  The  heat  rejected  by  the  high-pressure 
cylinder  during  exhaust  is 


This  heat  passes  into  the  first  intermediate  cylinder,  and  from 
thence  with  the  gain  or  loss  experienced  there  proceeds  to  the 
next  cylinder.  The  sum,  or  difference,  may  be  taken  for  Q  ', 
the  heat  brought  into  that  next  cylinder  per  stroke.  The  same 
operation  may  be  applied  to  each  successive  cylinder,  and  the 
result  may  be  checked  by  the  data  depending  on  the  condenser. 


CHAPTER   XIV. 

TESTING   STEAM-ENGINES. 

TESTS  of  steam-engines  are  made  either  to  find  the  cost  of 
power  or  to  study  the  transformations  of  heat  and  work  in  the 
engine,  though  both  objects  are  frequently  sought  in  the  same 
test.  The  cost  of  power  is  commonly  stated  in  pounds  of  coal, 
or  of  combustible,  per  horse-power  per  hour.  To  obtain  this 
cost  of  power  the  engine  and  boiler  must  be  considered  as  one 
system,  and  a  test  consists  essentially  in  weighing  the  coal 
consumed  and  measuring,  in  some  manner,  the  work  produced 
in  a  given  time.  The  power  may  be  measured  by  aid  of  steam- 
engine  indicators,  by  a  friction  brake,  or  by  a  transmission 
dynamometer  ;  the  measurement  of  the  fuel  consumed  must  be 
done  with  all  the  precautions  required  for  an  accurate  boiler 
test,  and  such  a  test  should  last  at  least  ten  hours.  Though  a 
test  of  this  kind  will  give  directly  the  cost  of  power  of  a  plant 
consisting  of  engine,  boiler,  etc.,  or  will  determine  which  of 
two  or  more  plants  is  the  most  economical,  it  does  not  give  the 
means  of  distinguishing  whether  the  excellence  or  defects  of  a 
system  are  due  to  the  engine  or  the  boiler,  much  less  does  it 
enable  us  to  make  such  an  analysis  as  will  show  why  a  given 
engine  or  boiler  is  better  than  another. 

To  distinguish  between  the  performance  of  the  engine  and 
of  the  boiler,  it  is  customary  to  state  the  performance  of  the 
boiler  in  pounds  of  water  evaporated  per  pound  of  fuel,  and 
that  of  the  engine  in  pounds  of  water  per  horse-power  per 
hour.  The  evaporative  efficiency  of  a  boiler  is  frequently 
stated  in  pounds  of  water  evaporated  per  pound  of  fuel,  from 
and  at  212°  F. ;  that  is,  a  special  thermal  unit,  equal  to  965.8 
B.T.U.,  is  employed.  For  example,  if  a  boiler,  for  each  pound 
of  fuel  consumed,  takes  eight  pounds  of  feed-water  at  60°  F., 

225 


226  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

and  evaporates  it  into  dry  steam  under  a  pressure  of  100 
pounds  to  the  square  inch  above  the  atmosphere,  then  it 
is  assumed  that  each  pound  of  fuel  can  evaporate 

8  X  1184.9 


pounds  of  water  at  212°  F.,  and  under  the  pressure  of  the 
atmosphere,.  No  attempt  has  been  made  to  put  the  steam 
consumption  of  engines  on  as  logical  a  basis,  and  in  general  it  is 
necessary  to  know  the  type  of  an  engine  and  the  conditions 
under  which  it  works  in  order  to  judge  whether  its  perform- 
ance is  good  or  not. 

It  is  in  general  better  to  make  an  engine  test  independent 
of  the  boiler  test,  especially  if  an  attempt  is  to  be  made  to  ana- 
lyze the  transformations  of  heat  and  work  ;  and  this  is  the  more 
convenient  as  an  engine  test  of  from  one  to  four  hours  in 
length  is  sufficient  under  favorable  conditions.  Even  though 
the  immediate  object  of  the  test  is  to  ascertain  the  steam  con- 
sumption only,  as  many  as  possible  of  the  data  mentioned 
in  Hirn's  analysis,  page  185,  should  be  taken  and  recorded  :  to 
wit,  the  pressure  and  condition,  whether  primed  or  super- 
heated, of  the  steam  supplied  to  the  engine,  together  with  the 
weight  of  the  same  ;  the  weight  and  initial  and  final  tempera- 
tures of  the  cooling  or  injection  water,  and,  where  a  surface  con- 
denser is  used,  the  temperature  of  the  water  resulting  from  the 
condensation  of  the  steam  ;  the  vacuum  in  the  condenser  and 
the  pressure  of  the  atmosphere  ;  where  the  engine  is  com- 
pounded, the  pressure  of  the  receiver  or  receivers,  when  nearly 
constant,  may  be  taken,  and  if  in  any  way  heat  is  added  to  or 
taken  from  the  steam  in  a  receiver,  such  heat  should  be  meas- 
ured if  possible  ;  if  any  cylinder  or  cylinders  have  steam-jack- 
ets, the  pressure  and  condition  of  steam  supplied  to  each  jacket, 
and  the  weight  and  temperature  of  the  water  condensed 
therein,  should  be  known  ;  indicator-diagrams  should  be  taken 
at  each  end  of  each  cylinder,  at  intervals  depending  on  the 
length  and  regularity  of  the  test  ;  the  total  area  of  the  indica- 
tor-diagrams should  be  measured,  and  also  the  areas,  down  to 


TESTING   STEAM-ENGINES.  22 :/ 

the  line  of  absolute  vacuum,  under  the  lines  of  admission,  to 
cut-off,  expansion,  exhaust,  and  compression.  When  an  engine 
is  steam-jacketed,  it  is  assumed  that  the  condensation  in  the 
jacket  or  jackets  when  the  engine  is  at  rest  is  a  measure  of 
the  loss  by  external  radiation,  conduction,  etc. 

Thermometers. — Temperatures  are  commonly  measured 
by  aid  of  mercurial  thermometers,  of  which  three  grades  may  be 
distinguished.  For  work  resembling  that  done  by  the  physic- 
ist the  highest  grade  should  be  used,  and  these  must  ordinarily 
be  calibrated,  and  have  their  boiling  and  freezing  points  deter- 
mined by  the  experimenter  or  some  qualified  person  ;  since 
the  freezing-point  is  liable  to  change,  it  should  be  redetermined 
when  necessary.  For  important  data  good  thermometers  must 
be  used,  such  as  are  sold  by  reliable  dealers,  but  it  is  pref- 
erable that  they  should  be  calibrated  or  else  compared  with 
a  thermometer  that  is  known  to  be  reliable.  For  secondary 
data  or  for  those  requiring  little  accuracy,  common  thermome- 
ters with  the  graduation  on  the  stem  may  be  used,  but  these 
also  should  have  their  errors  determined  and  allowed  for.  Ther- 
mometers with  detachable  scales  should  be  used  only  for  crude 
work. 

Gauges. — Pressures  are  commonly  measured  by  Bourdon 
gauges,  and  if  recently  compared  with  a  correct  mercury  col- 
umn, these  are  sufficient  for  engineering  work.  The  columns 
used  by  gauge-makers  are  commonly  subject  to  minor  errors, 
and  are  not  usually  corrected  for  temperature.  It  is  important 
that  such  gauges  should  be  frequently  retested.  From  their 
convenience,  vacuum  gauges  of  the  same  form  are  used,  even 
where  a  mercurial  gauge  could  easily  be  applied. 

The  pressure  of  the  atmosphere  may  be  taken  with  either  a 
mercurial  or  an  aneroid  barometer,  but  if  the  latter  is  used  its 
errors  must  be  known.  It  should  be  easy  to  make  the  baro- 
metric errors  only  a  fraction  of  the  unavoidable  gauge  errors. 

Dynamometers. — The  standard  for  measurement  of  power 
is  the  friction  brake.  For  smooth  continuous  running  it  is  es- 
sential that  the  brake  and  its  band  should  be  freely  lubricated 
with  oil,  and  that  the  cooling  should  be  done  by  a  stream  of 


228  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

water  that  does  not  come  in  contact  with  the  rubbing  surfaces. 
Sometimes  the  wheel  is  cooled  by  a  stream  of  water  circulating 
through  it,  sometimes  the  band  is  so  cooled,  or  both  may  be. 
A  rubbing  surface  which  is  not  cooled  should  be  of  non-con- 
ducting material. 

To  avoid  the  increase  of  friction  on  the  brake-bearings  due 

o 

to  the  load  applied  at  a  single  brake  arm,  two  equal  arms  may 
be  used  with  two  equal  and  opposite  forces  applied  at  the  ends 
to  form  a  statical  couple. 

With  care  and  good  workmanship  a  friction  brake  may  be 
made  an  instrument  of  precision  sufficient  for  physical  investi- 
gations, but  with  ordinary  care  and  workmanship  it  will  give 
results  of  sufficient  accuracy  for  engineering  work. 

All  forms  of  transmission  dynamometers  should  be  stan- 
dardized, and  should  have  their  errors  determined  by  compari- 
son with  a  friction  brake. 

Indicators. — Our  knowledge  of  the  errors  of  indicators, 
whether  of  kind  or  degree,  is  very  limited.  Preliminary  ex- 
periments seem  to  show  that  at  moderate  speeds,  i.e.,  those 
that  give  little  or  no  oscillation  of  the  piston  and  pencil  motion, 
the  largest  errors  are  due  to  backlash  and  pencil  friction.  The 
latter  may  be  reduced  by  making  the  pencil  pressure  light,  but 
there  is  no  remedy  for  the  former.  It  probably  does  not  intro- 
duce an  error  of  more  than  one  or  two  per  cent  in  the  diagrams 
taken  with  good  indicators. 

It  is  essential  that  the  reducing  motion  should  be  correct, 
and  that  the  indicator-cord  should  be  short.  The  communica- 
tion between  the  indicator  and  the  cylinder  should  be  short 
and  direct,  but  if  a  pipe  must  be  used  it  should  be  well 
wrapped  to  avoid  radiation. 

Scales. — Weighing  may  be  done  with  scales  adapted  to  the 
load.  They  should  be  tested  with  standard  weights. 

Weirs  and  Orifices. — When  possible,  the  quantities  of 
water  involved  in  an  engine  test  should  be  weighed  directly  ;  and 
by  proper  provision  of  large  tanks  and  scales,  and  with  large 
valves,  large  quantities  of  water  may  be  thus  determined. 
When  the  water  cannot  be  weighed  directly  it  may  be  meas- 


TESTING  STEAM-ENGINES.  22$ 

ured  in  tanks  of  which  the  volume  is  known  either  from  meas- 
urement or,  preferably,  by  filling  them  with  weighed  water. 

When  the  two  preceding  methods  do  not  apply,  the  water 
may  be  allowed  to  flow  over  a  weir  or  through  an  orifice,  and 
the  volume  and  weight  may  be  determined  by  the  usual 
hydraulic  methods.  If  the  weirs  or  orifices  are  small,  the  co- 
efficients of  flow  should  be  determined  by  direct  experiment. 

Steam  Consumption. — The  steam  consumption  of  an  engine 
is  preferably  determined  by  condensing  the  exhaust  steam  in  a 
surface-condenser  and  weighing  or  gauging  the  resulting  water. 
A  great  advantage  is  that  a  test  an  hour  or  two  long  is  then 
sufficient. 

When  the  exhaust  steam  cannot  be  thus  condensed  the 
boiler  or  boilers  supplying  the  engine  may  be  isolated  so  that 
all  the  steam  made  must  go  to  the  engine,  and  then  the  feed- 
water  supplied  to  the  boiler  may  be  weighed  or  gauged.  Af- 
ter the  engine  has  been  running  long  enough  to  come  to  its 
normal  condition,  the  height  of  the  water  in  the  boiler  gauge- 
glass  may  be  noted,  all  the  feed-water  during  a  test  of  from 
two  to  four  hours  in  length  may  be  weighed  or  measured,  and 
at  the  end  of  the  test  the  water  in  the  gauge-glass  must  be 
brought  to  the  initial  height. 

Calorimeters, — When  superheated  steam  is  supplied  to  an 
engine  it  is  sufficient  to  take  the  temperature  of  the  steam  in 
the  steam-pipe  near  the  engine.  When  moist  steam  is  used, 
the  condition  of  the  steam  must  be  determined  by  a  calorimet- 
ric  experiment.  Four  kinds  of  calorimeters  will  be  described 
out  of  a  large  number  that  have  been  used  by  different  experi- 
menters and  at  different  times.  They  are  the  barrel  calorime- 
ter, the  Barrus  continuous  water  calorimeter,  the  Barrus  super- 
heated steam  calorimeter,  and  the  throttling  calorimeter. 

The  Barrel  Calorimeter. — A  wooden  barrel  set  on  scales 
is  provided  with  a  large  valve  for  emptying  it,  and  provision  is 
made  for  filling  it  with  cold  water,  usually  from  a  hydrant  pipe, 
and  for  bringing  the  steam  to  be  tested.  Some  form  of  stirrer 
must  be  used,  a  good  form  being  a  wooden  propeller-wheel  on 
a  wooden  shaft  with  a  hand  crank. 


230  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  method  of  making  a  test  is  as  follows  :  The  barrel  is 
weighed  empty,  and  a  suitable  quantity  of  cold  water  is  run  in 
and  weighed.  The  temperature  of  the  cold  water  should  be 
taken  as  it  enters.  The  steam-pipe  usually  terminates  in  a 
piece  of  rubber  hose  which  may  be  swung  into  or  out  of  the 
barrel.  When  the  barrel  is  nearly  filled  with  cold  water,  the 
steam-valve  may  be  opened  until  all  condensed  water  is  blown 
from  the  pipe  and  the  hose  is  warmed  up  ;  then  the  hose  may 
be  swung  into  the  barrel  and  steam  may  be  run  into  the  water 
till  a  proper  amount  is  condensed.  A  preliminary  calculation 
will  determine  the  proper  weights  of  water  and  steam  to  give  a 
good  range  of  temperatures  in  the  calorimeter.  After  the 
steam  is  run  in,  the  water  in  the  barrel  maybe  well  stirred,  and 
the  highest  temperature  taken  as  the  final  temperature. 

To  eliminate  the  action  of  the  wood  of  the  barrel,  one  or 
more  tests  are  made  and  rejected,  and  the  times  of  running  in 
water  and  steam  are  made  equal,  so  that  the  barrel  which  is 
already  warmed  by  the  preceding  test  may  give  up  as  much 
heat  during  one  part  of  the  process  as  it  receives  during  the 
other  part. 

If  the  pressure  of  the  steam  is/,  and  the  part  of  each  pound 
of  the  mixture  which  is  steam  is  represented  by  x,  while  the 
initial  and  final  temperatures  of  the  water  are  tl  and  t^  ,  and 
the  weights  of  the  water  and  steam  are  W  and  wy  then 


(282> 


wr 


r  and  q  being  the  latent  heat  and  heat  of  the  liquid  for  the 
pressure/,  and  ql  and  q^  being  the  heats  of  the  liquid  for  the 
temperatures  tv  and  t^  . 

EXAMPLE.  —  Suppose  that  180  pounds  of  water  at  the  tem- 
perature of  60°.  2  F.  are  run  into  a  barrel  calorimeter,  and  that 
the  final  temperature  of  the  water  in  the  calorimeter  is  IO3°.6 
F.,  after  7^  pounds  of  steam  at  73.8  pounds  by  the  gauge  are 


TESTING   STEAM-ENGINES.  231 

run  in  and  condensed.  At  an  absolute  pressure  of  88.5 
pounds,  r  —  890.4,  q  —  288.8 ;  the  heats  of  the  liquid  at  6o°.2 
and  ic>30.6  are  28.32  and  71.6. 

180(71.6  -  28.32)-  7.25(288.8  -  71.6) 

"7.25  x  890.4  =°'963' 


consequently  the  per  cent  of  priming  is  3.7. 

It  is  to  be  remarked  of  this  kind  of  calorimeter  that  satis- 
factory results  are  difficult  to  attain  even  when  every  care  and 
precaution  are  used,  and  that  a  small  error  in  determining  the 
weight  of  steam,  which  is  obtained  by  subtraction,  makes  a 
large  difference  in  the  result. 

Barrus  Continuous  Water  Calorimeter.  —  The  difficulty 
of  obtaining  the  weight  of  steam  with  sufficient  accuracy,  which 
occurs  in  the  use  of  the  barrel  calorimeter,  is  avoided  in  the  use 
of  the  continyous  water  calorimeter  represented  by  Fig.  54. 
This  calorimeter  is  essentially  a  small  surface  condenser  of 
special  form,  so  arranged  that  the  condensed  steam  is  weighed 
separately  from  the  cooling  water. 

Steam  is  brought  to  the  calorimeter  by  the  .pipe/,  with  the 
gauge  i  for  giving  the  pressure.  The  pipe  a,  which  forms  the 
condensing  surface,  and  which  may  conveniently  be  made  of 
brass  pipe  one  inch  in  diameter,  should  have  the  joints,  above 
and  below,  clear  of  the  bucket  containing  the  cooling  water. 
Steam  is  let  into  the  pipe  a  at  full  boiler-pressure,  and  the  con- 
densed water  gathers  in  the  pipe  below,  where  the  water-level 
is  shown  at  e.  The  height  of  the  water  at  e  is  kept  constant 
by  aid  of  the  valve  at  d,  which  may  have  a  long  wooden  handle 
attached  for  convenient  regulation.  At  h  there  is  a  thermome- 
ter to  determine  the  temperature  of  the  condensed  steam.  Since 
this  temperature  is  only  a  little  less  than  that  due  to  the  boiler- 
pressure,  the  condensed  water  should  be  led  through  a  cooler 
like  a  simple  surface  condenser,  with  a  separate  stream  of  cool- 
ing water,  and  the  cooled  water  may  be  collected  and  weighed 
on  suitable  scales. 


232  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  cooling  water  for  the  calorimeter  is  brought  by  the 
pipe  b  with  a  valve  for  regulating  the  supply,  and  is  led  away 
to  a  barrel  on  scales  by  the  pipe  c,  with  a  valve  to  regulate  the 


COLD  WATER 


CONDENSED 
WATER 


FIG.  54. 

height  of  the  water  in  the  bucket.  To  insure  a  good  circula- 
tion and  a  proper  mingling  of  the  cooling  water  the  current  is 
directed  through  a  rubber  hose  to  the  bottom  of  the  inner  cylin- 
der around  the  pipe  a,  thence  up  and  into  the  top  of  the  outer 
cylinder,  thence  down  and  out  at  the  bottom  of  this  cylinder 


TESTING   STEAM-ENGINES.  233 

and  over  a  weir  at  the  exit.  The  temperatures  of  the  cooling 
water  at  entrance  and  exit  are  taken  by  the  thermometers  f  and 
g,  which  should  be  reliable  to  ^  of  one  degree  Fahrenheit. 

The  pipe/  leading  to  the  calorimeter  and  the  pipe  contain- 
ing the  condensed  steam  should  be  well  wrapped  as  far  as  to 
the  valve  at  d.  At  k  there  is  a  brass  cone  to  protect  the  cover- 
ing of  the  pipe  from  water. 

Though  not  essential,  it  is  convenient  to  line  the  bucket 
with  sheet  metal. 

In  preparing  for  a  test  the  water  and  steam  are  let  on  and 
properly  regulated,  and  the  calorimeter  is  allowed  to  run  till 
all  parts  may  be  assumed  to  be  at  a  constant  temperature ;  the 
cooling  water  from  c  and  the  condensed  steam  are  then  directed 
into  the  receptacles  for  weighing,  and  the  time  is  noted  as  the 
beginning  of  the  test.  The  steam-pressure  and  the  several  tem- 
peratures are  taken  at  intervals  and  recorded.  At  the  end  of 
half  an  hour  or  an  hour  the  cooling  water  and  condensed  water 
are  diverted  from  the  weighing  receptacles,  and  the  time  is  noted 
as  the  end  of  the  test.  The  quantities  of  the  cooling  and  con- 
densed water  can  be  weighed  at  the  end  of  the  test,  or  the  test 
may  be  made  continuous  for  any  desired  length  of  time  by  hav- 
ing two  weighing  receptacles  for  each,  and  filling  and  empty- 
ing them  alternately. 

The  radiation  in  thermal  units  per  hour  must  be  determined 
by  running  the  calorimeter  without  cooling  water  and  with  the 
bucket  filled  with  hair-felt. 

In  this  or  any  form  of  calorimeter  that  is  capable  of  giving 
accurate  results  it  is  essential  that  the  steam-pressure  should 
not  change  during  a  test,  since  a  considerable  change  of  pres- 
sure will  vitiate  the  results  on  account  of  the  heat  absorbed  or 
yielded  by  the  pipes  leading  to  the  condenser. 

Let  Wand  w  be  the  weights  of  the  cooling  water  for  the 
test,  and  let  /  be  the  steam-pressure,  and  tz  the  final  tempera- 
ture of  the  condensed  steam  taken  by  the  thermometer  at  //, 
while  /,  and  /,  are  the  initial  and  final  temperatures  of  the  cool- 
ing water ;  finally,  let  the  radiation  during  the  test  be  e  thermal 
units. 


234  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Then 


- 


EXAMPLE.  —  The  following  are  the  data  of  a  test  made  in  the 
laboratory  of  the  Institute  of  Technology  : 

Initial  temperature  of  cooling  water,   .     .  3/°.49  F. 

Final  "  "        "  "        .     .  83°.84  F. 

Temperature  of  condensed  steam,  .     .     .  304°.  88  F. 
Pressure  of  the  atmosphere,    .....       14.8  Ibs.  per  sq.  in. 

Pressure  of  steam  by  gauge,   .     .     .     .     .       72.4    "      "     "     " 

Duration  of  test,  .........       40  minutes. 

Radiation  per  hour,  .....     .     f     •  180  B.  T.  U. 

Weight  of  cooling  water,    ......  573-5  pounds. 

"        "  condensed  water,  .....       29.89     " 

x  _  573-5(5i-9I  -  5-53)  +  120-29.89(287.6-274.4) 
29.89  X  891.2 

x  —  0.988. 

Per  cent  of  priming,  1.2. 

It  is  apparent  that  any  surface  condenser  may  be  used  in 
the  same  manner,  as  a  calorimeter,  except  that  it  is  not  usually 
convenient  to  fill  such  a  condenser  with  steam  at  boiler-pres- 
sure. Since  the  wire-drawing  of  steam  in  a  well-wrapped  valve 
is  accompanied  with  little  loss  of  heat,  this  need  not  interfere 
with  such  a  use  of  a  condenser.  In  an  engine  test  the  quality 
of  exhaust  steam  flowing  to  either  a  jet  or  a  surface  condenser 
can  be  determined  by  equation  (282)  or  (283),  except  that  the 
external  radiation  cannot  always  be  satisfactorily  determined. 

Barrus  Superheated-steam  Calorimeter.  —  A  form  of 
calorimeter  devised  by  Mr.  Barrus  is  shown  in  Fig.  55,  which 


TESTING  STEAM-ENGINES. 


235 


determines  the  quality  of  steam  by  finding  how  much  heat  is 
required  to  superheat  it. 

The  steam  to  be  tested  comes  into  the  pipe  H  and  passes 
through  a  tubular  superheater  /,  and  flows  out  of  an  orifice  at 


SJEAM  TO  BE  TESTED 

i'piPE 


M.  A  separate  stream  of  steam  comes 
in  by  the  pipe  E,  is  strongly  super- 
heated by  gas  lamps  in  the  super- 
heater Gj  passes  around  the  tubes  of 
the  superheater  y,  and  flows  out  of  an 
orifice  at  N  of  the  same  diameter  as 
that  at  M.  Temperatures  are  taken 
by  the  thermometers  at  A,  B,  and  C\ 
and  the  boiler-pressure,  which  is  admit- 
ted to  all  the  apparatus,  is  measured 
by  a  gauge.  In  the  calculation  it  is  as- 
sumed that  the  specific  heat  of  super- 
heated steam  at  all  temperatures  and  pressures  is  cp  =  0.48  as 
determined  by  Regnault,  and  that  the  same  weight  of  steam 
will  flow  out  of  each  of  the  orifices  M  and  N  under  the  same 


ORIFICE  I.  DIA. 


236  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

pressure,  though  the  temperatures  are  different.  The  admissi- 
bility  of  the  last  assumption  can  be  tested  for  any  experiment 
by  condensing  and  weighing  the  steam  from  each  orifice  sepa- 
rately. 

The  radiation  from  this  calorimeter  may  be  formed  by 
allowing  the  superheating  steam  to  flow  through  the  super- 
heater/, while  the  moist  steam  to  be  tested  is  shut  off.  The 
difference  between  the  temperatures  given  by  the  thermometers 
at  A  and  B  under  such  circumstances  is  due  to  external  radia- 
tion, and  will  be  the  same  under  like  conditions  ;  let  this  loss 
be  n  degrees.  Let  the  initial  temperature  of  the  superheat- 
ing steam  be  ta  and  the  final  temperature  be  4.  Let  the  pres- 
sure of  the  steam  be/,  to  which  correspond  the  temperature  / 
and  latent  heat  r.  Let  tfte  steam,  which  at  first  had  the  tem- 
perature t  and  contained  I  —  x  of  moisture,  leave  the  orifice  M 
with  the  temperature  ts  .  The  heat  yielded  by  the  superheating 
steam  is  0.48(4  —  4),  of  which  0.48;*  is  lost  by  external  radia- 
tion. The  heat  gained  by  the  steam  under  test  is  (i  —  x)r 


Consequently, 

0.48(4  -tb-n)  =  (i-  x)r  +  0.48(4  - 


EXAMPLE. — The  following  are  the  data  of  a  test  made  with 
this  calorimeter  in  the  laboratory  of  the  Institute  of  Tech- 
nology : 

Pressure  of  the  atmosphere, 14.7  pounds  ; 

Gauge-pressure  of  steam, 7*-7       " 

Final  temperature  of  steam  to  be  tested,  .     .     .  331°. 8  F. 

Initial  temperature  of  superheating  steam,    .     .  4i7°-4  F. 

Final  "  "  "  .     .  347°4  F. 

Loss  of  temperature  by  radiation, n°.7F. 


TESTING   STEAM-ENGINES. 


237 


I  —  X  — 


o.4S[4i;.4  -  347-4  -  1 1-7  -  (331.8  -  317.2)]  . 


891.7 


i  —  x  —  0.024. 


It  was  found,  by  special  experiment  under  the  conditions  of 
the  experiment,  that  the  radiation  of  the  pipe  leading  to  the 
calorimeter  increased  the  moisture  in  the  steam  1.2  per  cent; 
consequently  the  priming  is  1.2  per  cent. 

Throttling  Calorimeter. — A  simple  form  of  calorimeter, 
shown  by  Fig.  56,  was  devised  by  the  author,  which .  depends 
on  the  property  that  dry  steam  is 
superheated  by  throttling.  Steam 
to  be  tested  is  brought  in  by  a 
wrapped  pipe  a,  below  which  the 
extension  c  with  a  drip  at  the  end 
serves  as  a  pocket  to  catch  the 
water  which  may  gather  on  the 
sides  of  the  pipe.  The  valve  at  b 
is  opened  a  slight  amount  to  admit 
steam  to  the  chamber  A,  and  the 
exit  valve  at  d  is  used  to  regulate 
the  pressure  in  the  chamber.  The 
temperature  in  the  chamber  is 
taken  by  a  thermometer  in  a  long 
cup  at  e,  and  the  pressure  is  taken 
by  the  gauge  f.  Let  the  boiler- 
pressure  be  /,  and  let  r  and  q  be  FIG.  56. 
the  latent  heat  and  heat  of  the  liquid  corresponding.  Let/, 
be  the  pressure  in  the  calorimeter,  and  A,  and  tl  the  total  heat 
and  the  temperature  of  saturated  steam  at  that  pressure,  while 
ts  is  the  temperature  of  the  superheated  steam  in  the  calorim- 
eter. Then 

xr  +  q  =  A,  +  cp(t,  -  t^  ; 


x  = 


(285) 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


EXAMPLE. — The  following  are  the  data  of  a  test  made  with 
this  calorimeter  : 

Pressure  of  the  atmosphere, 14.8  pounds  ; 

Steam-pressure  by  gauge, 69.8        " 

•     Pressure  in  the  calorimeter,  gauge,      .     .  12.0        " 

Temperature  in  the  calorimeter  :    .     .     .  268°. 2  F. 

x_\\  56.4  +  0.48(268.2  -  243.9)  -  286.3  _  Q    8g> 

% 

Per  cent  of  priming,  1.2. 

A  little  consideration  shows  that  this  type  of  calorimeter 
can  be  used  only  when  the  priming  is  not  excessive ;  otherwise 
the  wire-drawing  will  fail  to  superheat  the  steam,  and  in  such 
case  nothing  can  be  told  about  the  condition  of  the  steam 
either  before  or  after  wire-drawing.  To  find  this  limit  for  any 
pressure,  ts  may  be  made  equal  to  ^  in  equation  (285) ;  that  is, 
we  may  assume  that  the  steam  is  just  dry  and  saturated  at  that 
limit  in  the  calorimeter.  Ordinarily  the  lowest  convenient 
pressure  in  the  calorimeter  is  the  pressure  of  the  atmosphere,  or 
14.7  pounds  to  the  square  inch.  The  table  following  has-been 
calculated  for  several  pressures  in  the  manner  indicated.  It 
shows  that  the  limit  is  higher  for  higher  pressures,  but  that 
the  calorimeter  can  be  applied  only  where  the  priming  is  mod- 
erate. 

LIMITS  OF  THE  THROTTLING  CALORIMETER. 


PRESSURE. 

Absolute. 

Gauge. 

300 

285.3 

0.077 

250 

235-3 

0.070 

200 

185.3 

0.061 

175 

160.3 

0.058 

150 

135-3 

0.052 

125 

II0.3 

0.046 

IOO 

85-3 

0.040 

75 

60.3 

0.032 

50 

35-3 

0.023 

TESTING   STEAM-ENGINES.  239 

When  this  calorimeter  is  used  to  test  steam  supplied  to  a 
condensing  engine,  the  limit  may  be  extended  by  connecting 
the  exhaust  to  the  condenser.  For  example,  the  limit  at  100 
pounds  absolute,  with  3  pounds  absolute  in  the  calorimeter,  is 
0.064,  instead  of  0.046  with  atmospheric  pressure  in  the  calo- 
rimeter. 

In  case  the  calorimeter  is  used  near  its  limit, — that  is,  when 
the  superheating  is  a  few  degrees  only, — it  is  essential  that  the 
thermometer  should  be  entirely  reliable,  otherwise  it  might  hap- 
pen that  the  thermometer  would  show  superheating  when  the 
steam  in  the  calorimeter  was  saturated  or  moist.  In  any  other 
case  a  considerable  error  in  the  temperature  will  produce  an 
inconsiderable  effect  on  the  result.  Thus,  at  100  pounds  abso- 
lute with  atmospheric  pressure  in  the  calorimeter,  10°  F.  of 
superheating  indicates  0.035  priming,  and  15°  F.  indicates  0.032 
priming.  So  also  a  slight  error  in  the  gauge-reading  has  little 
effect.  Suppose  the  reading  to  be  apparently  100.5  pounds 
absolute  instead  of  100,  then  with  10°  of  superheating  the 
priming  appears  to  be  0.033  instead  of  0.032. 

Efficiency  of  a  Steam-engine. — When  the  performance 
of  an  engine  is  given  in  pounds  of  water  per  horse-power  per 
hour  it  is  necessary  to  know  also  the  pressure  and  quality  of 
the  steam  used,  and  also  to  know  the  temperature  of  saturated 
steam  at  the  pressure  against  which  the  engine  exhausts.  The 
difference  of  economy  to  be  expected  from  high-pressure  or 
low-pressure  steam,  from  superheated  or  wet  steam,  or  from  a 
condensing  or  non-condensing  engine,  are  specific  instances  of 
causes  modifying  the  performance  of  an  engine. 

There  appears  to  be  no  good  reason  why  the  performance 
of  an  engine  should  not  be  stated  in  thermal  units  per  horse- 
power per  hour,  which  would  enable  us  to  compare  directly 
all  forms  of  engines  without  allowances  or  reductions.  Such  a 
method  also  leads  at  once  to  the  consideration  of  the  true 
efficiency  of  an  engine. 

Suppose  that  an  engine  is  supplied  with  M  pounds  of 
steam  per  stroke,  having  the  pressure  /  and  the  quality  x. 


24O  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Then  the  heat  in  that  steam  above  the  heat  in  the  same  weight 
of  water  at  freezing  is 


Should  the  steam  be  superheated  and  have  the  temperature  ts 
then  the  heat  in  the  steam  is 


Let  the  pressure  against  which  the  engine  exhausts  be  p9  ,  at 
which  steam  has  the  temperature  t0  and  the  heat  of  the  liquid 
qQ  .  If  the  engine  is  a  condensing  engine  the  water  in  the  hot- 
well,  from  whence  the  boiler  is  fed,  can  have  nearly  this  tem- 
perature, and  if  the  engine  is  non-condensing,  then  the  feed- 
water  can  be  raised  nearly  to  this  temperature  by  an  exhaust- 
steam  feed-water  heater.  It  may  be  considered  that  the  heat 
furnished  to  the  engine  per  stroke  is,  for  moist  steam, 


and  that  amount  of  heat  must  in  general  be  given  to  the  water 
and  steam  in  the  boiler  by  the  fire. 

The  work  done  by  the  steam  per  stroke,  shown  by  the  in- 
dicator, is  W,  the  heat  equivalent  is  A  W.  The  efficiency  of 
the  engine  is  consequently 

A  W 

*<=  •  •  •  •  •  <286> 


When  d,  the  consumption  of  steam  per  indicated  horse- 
power per  hour,  is  stated,  the  efficiency  is 

60  X  33QQQ  X  A 
*?*  —  'r(~J~\~       TT v25' ' 


The  last  two  equations  give  the  efficiency  of  the  fluid.   The 
efficiency  of  the  engine,  determined  by  aid  of  a  brake  or  dyna- 


TESTING   STEAM-ENGINES,  241 

mometer,  is  found  by  substituting  for  Ci}  Cn  the  consumption 
of  steam  per  net  or  brake  horse-power  per  hour,  so  that 

60  X  330QQ  X  A 
nn  =  -7^-7  -  :  -  r  ...... 


Similar  equations  may  be  deduced  for  superheated  steam. 
The  two  efficiencies  77,-  and  rjb  are  to  be  compared  with  the 
maximum  efficiency 


T-  T0 


of  a  heat-engine  working  between  the  temperatures  T  and  T0  , 
the  absolute  temperatures  of  saturated  steam  at  the  pressures 

P  and  A  • 

Efficiency  of  the  Boiler.  —  If  the  total  heat  of  combustion 
of  the  fuel  is  H  thermal  units  per  pound,  and  if  one  pound  of 
fuel  evaporates  m  pounds  of  water  from  the  temperature  t^  T 
which  may  or  may  not  be  equal  to  /„  ,  to  form  steam  having 
the  quality  x,  at  the  pressure/,  then  the  efficiency  of  the  fur- 
nace and  boiler  is 


H 


(2 


Efficiency  of  Engine  and  Boiler.  —  The  efficiency  of  the 
engine  and  boiler  combined  is  the  product  of  the  efficiencies 
of  each  separately  ;  that  is, 


Cost  of  Power.  —  The  evaporative  efficiency  of  a  boiler  is 
commonly  given  in  pounds  of  water  evaporated  from  and  at 
212°  F.,  equivalent  to  965.8  B.  T.  U.  per  pound  ;  so  that  if  m  is 
the  actual  evaporation  as  used  above,  and  mQ  the  reduced  evap- 
oration, 


16 


242  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Here  also  it  would  very  much  simplify  matters  if  thermal 
units  were  used  ;  and  then,  without  reduction,  the  evaporative 
efficiency  could  be  given  in  thermal  units  per  pound  of  fuel, 
which  could  be  compared  directly  with  the  total  heat  of  com- 
bustion. 

If  the  consumption  of  steam  per  net  horse-power  per  hour 
is  Cn  pounds,  so  that  the  consumption  of  heat  per  horse-power 
per  hour  is 

Cn(xr  +  $-  ?0), 

then  the  consumption  of  coal  per  horse-power  per  hour  is 
Cn(xr  +  q-q^>  ___  Cn(xr  +  q  -  q0] 


m(xr  +  q—q 


^  9  ' 


Efficiency  Test.  —  The  difficulty  of  arranging  for  the  com- 
plete testing  of  large  engines  that  are  in.  continuous  use  has 
led  to  the  proposal  of  a  simple  method  by  which  the  efficiency 
given  by  equation  (286)  may  be  found.  The  engine  is  indi- 
cated to  determine  A  W,  the  work  of  the  steam  per  stroke,  and 
the  condensing  water  and  condensed  steam  delivered  by  the 
air-pump  per  stroke  of  the  engine,  from  the  jet  condenser, 
flows  in  a  well-mixed  stream  over  a  weir.  If  G  is  the  injection- 
water  per  stroke,  and  M  the  steam  used  per  stroke,  then  this 
gives 

M  -\-  G  =  numerical  quantity,     v;  '/."   .     (292) 

The  initial  and  final  temperatures  /0  and  th  of  the  injection- 
water  are  taken  by  the  aid  of  thermometers. 
Of  the  heat 

M(xr  +  ?-?„) 

consumed  by  an  engine  per  stroke,  a  part,  A  W,  is  changed 
into  work,  a  part,  Qe,  is  lost  by  external  radiation,  and  the  re- 
mainder, G(qk  —  ^0),  is  carried  away  by  the  injection-water,  so 
that 

q).     .     (293) 


TESTING  STEAM-ENGINES.  243 


In  equation  (293),  W,  qk  ,  and  qQ  are  determined  directly,  r 
and  q  are  known  from  the  steam-pressure,  and  x  may  be  deter- 
mined by  calorimetric  experiment,  or  may  be  known  approxi- 
mately from  previous  experiments  under  like  conditions  ;  also, 
Qe  may  be  known  or  determined.  Under  good  conditions  x  is 
unity  or  differs  but  little  from  unity,  and  Qe  is  small,  so  that  it 
may  be  neglected  without  serious  error.  We  have  then,  for  an 
approximate  result,  two  equations  (292)  and  (293)  with  two  un- 
known quantities,  and  may  solve  for  M  directly,  and  therefrom 
estimate  the  steam  per  horse-power  per  hour,  or  by  equation 
(286)  may  find  the  efficiency. 

The  chief  advantage  of  this  method  is  that  it  need  not  in- 
terfere with  the  ordinary  running  of  the  engine  tested,  and 
does  not  require  much  time  or  trouble. 


CHAPTER   XV. 

TESTS   OF   SIMPLE   STEAM-ENGINES. 

IN  this  chapter  and  the  three  following  chapters  will  be 
given  the  data  and  results  of  several  series  of  steam-engine 
tests,  which  were  made  to  determine  the  relative  economy 
of  different  methods  of  running  engines  and  of  different  types 
of  engines. 

Tests  on  the  Michigan. — In  1861  experiments  were  made 
on  the  engines  of  the  United  States  paddle-wheel  steamer 
Michigan,  at  Erie,  Pa.,  by  a  board  of  naval  engineers,  and  re- 
ported by  Isherwood,*  to  determine  the  advantageous  point 
of  cut-off  for  naval  engines  of  that  type. 

This  vessel  had  a  pair  of  inclined  direct-acting  engines,  with 
a  jet  condenser,  and  with  the  form  of  poppet-valves  commonly 
used  on  American  steamboats,  but  with  the  Sickles  cut-off 
gear,  by  which  the  cut-off  could  be  varied  from  the  commence- 
ment of  the  stroke  to  -J  of  the  stroke ;  and  further,  the  cut-off 
could  be  varied  from  T7¥  to  -J-j-  of  the  stroke  when  the  special 
cut-off  gear  was  disconnected. 

The  steam-pipe  and  cylinder  sides  were  covered  with  felt 
and  lagged  with  wood ;  the  cylinder-heads  were  uncovered ; 
the  steam-pipes  were  so  inclined  that  they  drained  into  the 
cylinders.  The  main  dimensions  of  the  engines  were : 

Diameter  of  cylinder,    . 36  in. 

Diameter  of  piston-rod, 3f  in. 

Stroke  of  piston, 8  ft. 

Piston  displacement,  allowing  for  piston-rod,  56.544  cu.  ft. 

Clearance, 3.280  cu.  ft. 

Net  area  of  steam-valves, 1 14.96  sq.  in. 

Net  area  of  exhaust-valves,    ....»'.  108.38  sq.  in. 


*  Experimental  Researches  in  Steam  Engineering. 

244 


TESTS  OF  SIMPLE   STEAM-ENGINES.  245 

Diameter  of  paddle-wheel,     .     .     i    ..     .     .  2ij- ft. 

Number  of  paddles, *     *     .     .  16 

Width  of  paddles,     .........  31  in. 

Length  of  paddles, 14  ft. 

There  were  two  rectangular  internally  fired  boilers,  with 
vertical  water  tubes,  each  boiler  having  three  furnaces.  The 
boilers  were  of  the  type  known  as  Martin  boilers,  which  were 
nfuch  used  in  the  navy. 

Manner  of  making  Experiments. — The  number  of  revo- 
lutions was  recorded  by  a  counter  actuated  by  the  engine. 
The  feed-water  was  measured  in  a  zinc-lined  tank  that  held  70 
cubic  feet.  It  was  filled  from  the  hot-well  through  a  hose  by 
the  bilge-pump ;  and  there  was  a  small  hand-pump  that  was 
used  to  bring  the  level  to  the  reference-mark  each  time  with 
water  from  outside  the  vessel.  The  water  was  drawn  from  the 
tank  by  a  feed-pump  and  distributed  to  the  boilers.  All  con- 
nections to  the  boiler  were  broken  and  stopped  with  iron 
plates,  and  the  hose  from  the  bilge-  and  hand-pumps  were 
thrown  out  of  the  tank  after  it  was  filled.  The  tank  was 
pumped  dry  each  time,  and  the  feed-pipe  emptied.  The  tem- 
perature in  the  tank  was  noted  when  it  was  half  full. 

The  coal  was  weighed  on  scales  in  equal  portions.  Refuse 
was  weighed  dry  on  the  same  scales  and  in  the  same  manner. 

The  steam-pressures  were  measured  by  a  spring-gauge  and 
a  siphon  mercurial  gauge,  the  indications  of  which  coincided. 
The  vacuum  was  measured  with  a  similar  gauge.  The  atmos- 
pheric pressure  was  measured  by  an  aneroid  barometer,  and 
the  temperature  was  taken  from  a  thermometer  attached 
thereto.  Two  indicators  were  attached  permanently  to  the 
two  ends  of  the  cylinder,  and  were  actuated  from  the  air- 
pump  cross-head  by  a  reducing  lever. 

The  temperature  of  the  injection-water  was  taken  by  a  ther- 
mometer on  the  side  of  the  vessel  opposite  the  hot-well  discharge. 
The  temperature  of  the  hot-well  was  taken  by  a  thermometer 
immersed  in  it.  The  temperature  of  the  external  air  was  taken 
on  deck. 


246  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

The  boilers  were  fitted  with  gauge-cocks  and  glass  water- 
gauges.  The  only  outlet  from  the  boilers  was  through  the 
blow-off  valve ;  and  any  leakage  would  have  to  pass  also  a 
stop  cock  and  a  Kingston  valve. 

The  vessel  was  secured  to  the  dock,  and  was  housed  in,  and 
the  power  of  the  engine  was  expended  in  paddling  the  water 
aft.  Each  experiment  lasted  72  hours,  during  which  the  con- 
dition of  working  was  not  changed  in  any  way.  In  anticipa- 
tion of  the  experiment,  the  engine  was  run  several  hours  to 
bring  it  to  the  normal  working  condition.  When  all  was  ready, 
with  average  fires  and  proper  steam-pressure  and  level  of  water 
in  the  glass  gauges,  the  experiment  was  begun.  During  the 
experiment  the  working  of  the  engine  was  made  as  regular  as 
possible,  and  at  the  end  of  the  72  hours  all  conditions  were  left 
as  at  the  beginning.  The  fires  were  cleaned  at  beginning 
and  end ;  and  it  was  thought  that  the  error  from  this  source 
for  a  run  of  such  a  length  was  small.  The  steam-pressure 
varied  not  more  than  half  a  pound  during  the  entire  experi- 
ment. 

Indicator-diagrams  were  taken  every  half-hour,  and  each 
diagram  measured  separately.  During  all  the  experiments  the 
throttle-valve  was  wide  open,  and  the  boiler-pressure  was  varied 
so  as  to  keep  the  initial  pressure  in  the  cylinder  constant. 

At  the  end  of  the  experiments  the  paddles  were  removed 
from  the  wheel,  and  the  mean  pressure  then  required  to  move 
the  engine  was  used  in  allowing  for  the  friction  of  the  engine 
and  calculating  the  net  power. 

The  tightness  and  freedom  from  leakage  of  piston,  valves, 
and  stuffing-boxes  was  determined  several  times. 

The  temperature  of  the  gases  in  the  up-take  was  noted  by 
a  high-grade  mercurial  thermometer,  and  was  about  520°  F. 

Three  sets  of  observers  with  regular  duties  were  arranged 
in  watches,  each  superintended  by  a  chief  engineer  of  the  navy. 

The  data  and  results  of  the  experiments  are  given  in 
Table  I.  The  table  will  be  understood  from  the  headings 
with  very  little  added  explanation.  In  order  to  make  the  re- 
sults of  the  different  experiments  directly  comparable,  the 


OF  SIMPLE   STEAM-ENGINES. 


247 


TABLE  I. 
TESTS  ON  THE  UNITED  STATES  STEAMER  MICHIGAN. 

Pressures. 

Pounds  per  square  inch. 

•spunod 
L-z  jo  9ans 
-S9jd  jpsq 

(    V       |Bttb9  JOJ  J9p 

8  M   ^  g,  Lo  S 

woo  -*-0  r^roON 

ro  W    N    <M    W    « 

"I 

•^UOW 

O    ON  tv  ON  N    ONNO 
ro  -f  t^  H    N    t^  « 
ro  N    M    <M    <N    HI    N 

9jnSS9jd  9AIJ 
-09jp  UB9J\[ 

00  NO   M   ON-^VOOO 
ON  tx  ^  ON  t~>  rooo 

•g^ojjs  jo  pu3  vs 

J3JBAV  JO  1U90  J9J 

M    -^-OO  NO    M    M    O 

„=% 

ft  in  o  O  t-oo  tx 

| 
1 

o. 

e 

rt 

Modified. 

''3N 

O  NO   1000   ON  ro  W 
•*»•  ro  ro  ro  ro  ••<*•  10 

ajloj;s  jo  pug 

ON  ti    10  M    6\  tx  10 

S     M     H.     M 

•p91BOIpUJ 

OS  I-  iH  —  '  i-l  «  N 

oc  es  «i  •*  <*  w  i-i 

se  ce  ea  se  s;  es  •* 

"TSo 

Actual. 

•}9N 

ONNO    W    CO  N  OO    1O 
«'    t^-NO    <j>  ON  C"  O 

„ 

•:i  i-  r  —  —  r;  '•: 

•*  SS  t>.  e  r-  05  GO 

OS  •*  99  »O  ^  t»  ?D 

eoMecosseos-* 

•3jn[osqu 
^BWUI 

im& 

Horse-power. 

Modified. 

•«K 

l,s?vs  HI 

10  0    O*  HI    ^-  ro  CO 
ON  O  00    N    O  NO    10 

•ajgqdsoorn? 

O   10  O    0   O    O    O 

OTI 

•*  IOVO    tv  Tj-  10  M 

O     O  NO     tS     CO  ON  f) 

VO   ON  O-  t-*  -<f  O  00 

Inches  of  Hg. 

M9SU9pUOD 

ui  innnoBA 

vo  H  rooo  oo  NO  H 

1s'!S?R* 

^1^  SS'S'cT 

Actual. 

•19N 

ON  t^  ON  <N    O  NO    tx 
OO    ui  0    O    •<*•  CONO 
-     t^NONO     M     0     CO 

O     ThNO     ON  -^    rONO 
00    O^OO    HI    O  VO    •<*• 

•J919UIOJBg 

M  ro  M  •«•  10  1000 

w  00    t->  HI  OO  00  OO 

co  <N  N  ro  (N  N  N 

_: 

M   NO      HI      N      Tt-    t^    O 

co  ON  CN   HI   ro  TI-  5 

Temperatures,  Fahrenheit. 

•ipM-iojj 

8888888 

M   o   •*•  rooo  •*•  O 
O    w    O    ro  M    txNO 

•J9JBM-UOi;09Cui 

S2S2CO-CO-3 

Consumption,  pounds  per  hour. 

•31VJ3  JO  JOOJ 

3JBnbs  J9d  IBO^ 

CN    M     H?0^"  M  ^ON  H? 

oo  H!  o^o  to  ro  •<*• 

•^p^ 

£***»»• 

•9SHJ9J 
JO  JU30  J9J 

0?  10  ON  ON  ro  JC  ON 
VO  OO  VO    IONO    IOVO 

•raooj-9uiSug 

VO   lOOO   10  ON  tx  tv 

•iM 

ON  0    ON  tv-^-  O    t-. 

.00 

^  ^  rooo  O   t^  •*• 

J3ds^-a 

ON  HI    M    O  OO  00    O 
O  NO  00    ONNO  NO    0 
NO    1O  N  NO  OO    HI    H 

w«« 

O  10  N  fs  ro  M  vo 
•**•  CONO   O  oo  NO   O 
8ro  t^  I-N  O   t^oo 
[x.vO    •<»•  •q-  M    M 

0. 

•»o-ln0 

****** 

,  Pressures. 

g 

a 

(T. 

•p 

•uoisuedxa 
oi[oqj9dAq 

00  NO    ON  •*•  10  IO  ON 

•sjnoq  ui  uopejnQ 

isM  *  s  *.  j 

u^ouj  joj  sqi 

CM    CO  CO  M    rONO    t^ 

1 

-,,::---:.,- 

248  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

mean  effective  pressure  and  the  net  effective  pressures  are  given 
in  a  modified  form,  with  the  assumption  of  a  uniform  back  pres- 
sure of  2.7  pounds,  and  of  a  pressure  to  move  the  engine  un- 
loaded of  2.1  pounds.  The  modified  horse-power  and  consump- 
tion per  horse-power  per  hour  are  calculated  on  the  same  basis 
from  the  modified  pressures. 

Discussion  of  Results. — All  the  experiments  were  made 
on  the  starboard  engine,  the  other  one  being  disconnected. 

In  all  the  experiments  the  initial  pressure  in  the  cylinder 
was  maintained  constant,  and  the  boiler-pressure  was  varied 
slightly  for  that  purpose,  but  not  enough  to  affect  the  results 
materially.  The  speed  of  the  engine  could  not  be  controlled 
at  the  same  time,  but  the  variation  from  1 1  to  20  revolutions 
could  not  interfere  with  the  comparability  of  the  results. 

The  per  cent  of  water  in  the  cylinder  at  the  end  of  the 
stroke  is  not  excessive  for  a  cut-off  at  ^J  of  the  stroke.  It  in- 
creases rapidly  to  the  cut-off  at  -J,  then  it  remained  nearly  con- 
stant to  the  cut-off  at  J,  and  then  increased  again  at  a  cut-off 
at  -fe  of  the  stroke. 

The  consumption  of  steam  per  horse-power  per  hour  is  prop- 
erly a  basis  of  comparison  in  these  tests,  since  the  boiler-pres- 
sure did  not  vary  greatly  during  the  tests.  Since  the  variation 
of  the  back  pressure  is  due  either  to  a  variation  in  the  vacuum 
or  to  defects  in  the  valve-gear  or  steam  passages,  and  since  an 
engine  designed  for  a  given  expansion  may  be  supposed  to 
have  adequate  provision  for  maintaining  a  good  vacuum,  and 
for  realizing  it  in  the  cylinder,  it  appears  proper,  to  compare  the 
steam  consumption  corrected  for  variation  of  back  pressure, 
and  called  the  modified  steam  per  horse-power  per  hour  in  the 
tables. 

The  minimum  consumption  of  steam  per  indicated  horse- 
power per  hour  was  found  with  a  cut-off  at  -J  of  the  stroke, 
but  it  appears  that  the  consumption  is  nearly  the  same  for  all 
points  of  cut-off  from  J  to  T7¥  of  the  stroke. 

Comparing  the  consumptions  per  net  horse-power  per  hour, 
the  minimum  is  also  at  -J  of  the  stroke  in  the  table,  but  as  the 
consumption  for  shorter  cut-off  increases  rapidly  and  as  no  ex- 


TESTS  OF  SIMPLE   STEAM-ENGINES.  249 

periments  were  made  with  the  cut-off  intermediate  between  f 
and  T7Q- ,  the  most  advantageous  point  of  cut-off  may  be  longer 
than  $  of  the  stroke ;  and  this  seems  not  improbable,  since  the 
consumption  with  the  cut-off  at  -^  of  the  stroke  exceeds  the 
consumption  when  the  cut-off  is  at  f  of  the  stroke  by  2  per 
cent  only. 

Considering  the  relative  sizes  of  cylinders  for  the  develop- 
ment of  the  same  power,  Isherwood  concludes  that  for  naval 
engines  of  this  type  and  using  saturated  steam  at  a  pressure  of 
20  pounds  above  the  atmosphere,  it  is  advisable  to  use  a  cut- 
off at  JL.  of  the  stroke,  more  especially  as  a  special  cut-off  gear 
is  not  required  in  such  case. 

Later  experiments  on  engines  using  higher  pressure  of 
steam  show  that  the  advantageous  point  of  cut-off  becomes 
shorter  and  the  number  of  advisable  expansions  becomes 
greater  as  the  pressure  increases. 

It  is  instructive  to  notice  that  the  per  cent  of  water  in  the 
cylinder  at  the  end  of  the  stroke  increases  as  the  cut-off  is 
shortened,  and  that  with  the  exception  of  Experiment  5, 
which  for  some  reason  has  a  greater  consumption  of  steam 
than  either  the  test  preceding  or  following,  the  increase  is 
quite  regular.  It  appears  that  the  condensation  and  re-evapo- 
ration and  the  exhaust  waste  in  this  type  of  engine,  with  low- 
pressure  steam,  very  quickly  counteract  the  gain  to  be  antici- 
pated from  expansion. 

Tests  on  the  Mackinaw. — The  tests  on  the  engine  of  the 
United  States  steamer  Mackinaw  were  made  by  a  board  of 
naval  engineers*  to  determine  the  advantage  of  using  super- 
heated instead  of  saturated  steam,  and  at  the  same  time  an  in- 
vestigation was  made  to  determine  the  best  point  of  cut-off. 
The  Mackinaw  was  one  of  a  number  of  paddle-wheel  steamers 
built  for  special  service  during  the  years  1863  and  1864.  It 
had  one  direct-acting  inclined  engine,  with  poppet-valves  and  a 
Stevens'  cut-off.  The  engine  was  furnished  with  a  surface  con- 
denser. Steam  was  supplied  by  two  Martin  water-tube  boil- 

*  Experimental  Researches  in  Steam  Engineering. 


THERMODYNAMICS  OF  THE   STEAM-ENGINE. 

ers,  each  having  five  furnaces.     The  principal  dimensions  of 
the  engine  were : 

Diameter  of  cylinder,     .     .     .     .     .     .     .  4  ft.  10  in. 

Stroke  of  piston, 8  ft.  9  in. 

Diameter  of  piston-rod, 6J  in. 

Displacement  of  piston  allowing  for  rod, .  159.5356  cu.  ft. 

Clearance, 13.5254  cu.  ft. 

Area  for  admission  and  exhaust  of  steam,  393  sq.  in. 

Diameter  of  paddle-wheel, 26  ft. 

Number  of  paddles, 24 

Length  of  paddle, 9  ft. 

Width  of  paddle, I  ft.  3  in. 

Total  grate-area, 200  sq.  ft. 

Total  water-heating  surface, 5036  sq.  ft. 

Superheating  surface  in  up-takes,     .     .     .  171  sq.  ft. 

The  experiments  were  made  with  the  boat  secured  to  the 
dock  in  the  same  manner  and  with  the  same  precautions  as 
those  on  the  Michigan.  The  first  five  were  made  with  the 
water-level  at  the  normal  height,  so  that  the  steam  was  prob- 
ably saturated.  The  last  two  were  made  with  the  water  from 
five  to  six  inches  below  the  upper  ends  of  the  vertical  water- 
tubes,  so  that  the  steam  was  superheated. 

The  first  five  experiments  were  intended  to  be  at  the  same 
speed  of  revolution  of  the  paddle-wheels,  but  the  number  of 
revolutions  fell  to  5.609  per  minute  when  the  cut-off  was  at  0.21 
of  the  stroke  in  Experiment  E,  and  Experiment  A  was  made 
with  5.551  revolutions  for  sake  of  comparison. 

The  data  and  results  are  given  in  Table  II,  and  after  the 
discussion  of  previous  work  require  no  explanation  beyond 
that  given  by  the  headings. 

Discussion  of  Results. — Isherwood,  in  reporting  these 
experiments,  recalculated  the  results  of  the  tests  B,  C,  D,  and 
E,  on  the  following  assumptions : 

(i)  That  the  initial  pressure  was  50  pounds  absolute,  and 
the  pressure  at  cut-off  was  47  pounds  absolute. 


TESTS  OF  SIMPLE   STEAM-ENGINES. 


25  1 


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2$2  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

(2)  That  the  back  pressure  was  2  pounds,  and  the  pressure 
to  overcome  the  friction  of  the  engine  was  i|-  pounds. 

(3)  That  the  mean  total  pressure  was  the  same  per  cent  of 
the  initial  pressure  as  it  was  in  the  actual  experiment. 

The  results  are  given  in  the  following  table : 

B.  C.  D.  E. 

Cut-off, 0.70  0.56  0.38  0.21 

Number  of  expansions,       1.38         1.68         2.33         3.68 

Consumption  per  net  horse-power  estimated,     33.748     31.948     31.621     38.485 
Ratio  of  cylinders  for  equal  powers,      .     .     .       i.oo         1.05          1.24         1.59 

An  inspection  of  this  table,  or  of  the  results  in  Table  II,  in- 
dicates that  the  consumption  of  steam  per  horse-power  per  hour 
is  least  with  the  cut-off  at  0.38  per  cent  of  the  stroke,  but  that 
the  consumption  is  but  little  greater  with  the  cut-off  at  0.56  of 
the  stroke.  It  consequently  appears  that  the*advisable  cut-off  is 
at  half-stroke  or  a  little  later,  the  difference  between  the  results 
of  this  series  of  tests  and  the  results  of  the  tests  on  the  Michi- 
gan being  attributable  to  the  difference  of  steam-pressure. 

.The  last  two  tests  were  made  with  superheated  steam,  ob- 
tained by  running  with  the  water-level  in  the  Martin  vertical 
water-tube  boilers  below  the  tops  of  the  tubes,  so  that  of  the 
4036  square  feet  of  heating  surface  about  1000  square  feet  were 
available  for  superheating. 

In  these  experiments  the  number  of  revolutions  per  minute 
was  increased  by  removing  a  part  of  the  paddles.  In  Experi- 
ment F  the  steam  was  strongly  throttled,  but  in  Experiment  G 
the  throttle-valve  was  wide  open. 

If  it  be  admitted  that  Experiments  F  and  B  may  be  com- 
pared, then  the  gain  in  consumption  of  steam  per  indicated 
horse-power  per  hour  is 

32.913-  24.59  = 

32.913 
A  like  comparison  of  Experiments  E  and  G  shows  a  gain  of 

36.044  -  22.725  = 

36.044 

» 

by  the  use  of  superheated  steam. 


TESTS  OF  SIMPLE   STEAM-ENGINES.  253 

It  is  to  be  remembered  that  the  apparent  gain  from  super- 
heating is  obtained  while  the  engine  is  running  nearly  three 
times  as  fast,  and  exerting  nearly  three  times  the  power  that  it 
did  when  using  moist  steam. 

Tests  on  the  Eutaw. — The  steamer  Eutaw  was  one  of  the 
same  class  as  the  Mackinaw,  and  differed  only  in  that  the  cylin- 
der had  two  piston-rods  instead  of  one,  and  that  the  boiler  was 
furnished  with  a  tubular  superheater  in  the  up-take,  so  arranged 
that  the  engineer  could  use  saturated  steam,  superheated  steam, 
or  a  mixture  of  saturated  and  superheated  steam ;  more  prop- 
erly, the  mixing  of  the  two  kinds  of  steam  gave  a  ready  method 
of  controlling  the  degree  of  superheating.  The  piston  displace- 
ment was  159.2258  cubic  feet,  but  the  clearance  was  the  same 
as  for  the  Mackinaw. 

The  heating  surface  of  the  Martin  boilers  was  so  efficient 
that  the  products  of  combustion  in  the  up-take  were  only  40 
to  80  degrees  above  the  temperature  due  to  the  saturated 
steam  in  the  boilers,  so  that  to  make  a  provision  for  superheat- 
ing the  steam  efficiently  almost  all  of  the  water-tubes  were 
removed  from  one  furnace,  and  the  tubular  superheater  was 
placed  in  the  space  thus  provided. 

The  experiments  were  made  at  Washington  by  a  board  of 
naval  engineers,*  with  the  vessel  secured  to  the  dock.  It  was 
intended  that  the  steam-pressure  should  be  the  same  through- 
out, and  that  the  wheels  should  make  the  number  of  revolu- 
tions per  minute  that  the  power  would  give. 

Each  experiment  lasted  72  hours,  and  was  made  with  the 
usual  care  and  precautions  required  to  give  reliable  results.  It 
is  believed  that  there  was  no  leakage  from  the  boiler  nor  in 
the  cylinder,  and  that  there  was  no  priming. 

With  natural  draught  on  the  superheater,  the  temperature 
of  the  superheated  steam,  as  in  F  and  G,  was  about  360  de- 
grees, while  the  temperature  of  the  saturated  steam  was  270 
degrees,  giving  90  degrees  of  superheating.  When  the  blower 
was  applied  to  the  furnace  connected  with  the  superheater  the 
temperature  was  (H,  I,  and  J)  about  390  degrees,  showing 

*  Experimental  Researches  in  Steam  Engineering. 


254 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


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TESTS  OF  SIMPLE   STEAM-ENGINES.  255 

about  1 20  degrees  of  superheating.  The  highest  degree  of 
superheating  did  not  appear  to  injure  the  metal  of  the  cylin- 
der. 

Discussion  of  Results. — At  the  time  when  these  experi- 
ments were  made,  certain  steamers  plying  on  the  Chesapeake 
Bay  had  superheating  apparatus,  and  used  strongly  super- 
heated steam  mixed  with  moist  steam.  It  was  claimed  that 
a  great  economy  was  realized  from  the  use  of  such  mixed 
steam.  In  reality  the  whole  apparatus  was  only  a  means  of 
using  superheated  steam  of  which  the  degree  of  superheating 
could  be  controlled,  and  a  comparison  of  the  consumption  of 
superheated  steam  per  horse-power  per  hour  for  Experiments 
F  to  J  with  the  consumption  for  Experiments  K  to  O  indi- 
cates that  the  differences,  which  are  sometimes  on  one  side 
and  sometimes  on  the  other,  are  due  to  the  differing  degrees 
of  superheating  and  to  the  different  initial  pressures ;  further- 
more, the  differences  are  all  small,  and  in  many  cases  are  within 
the  probable  error  of  the  experiments. 

The  smallest  consumption  of  saturated  or  moist  steam  per 
horse-power  per  hour  was  obtained  in  Experiment  B,  with  a 
cut-off  at  0.32  of  the  stroke;  but  the  consumption  at  0.50  of 
the  stroke  being  but  little  larger,  it  may  be  concluded  as  in 
the  discussion  of  the  tests  on  the  Mackinaw  that  the  cut-off 
may  be  chosen  at  about  half-stroke. 

The  smallest  consumption  of  superheated  steam  per  horse- 
power per  hour  appears  to  have  been  obtained  with  the  cut-off 
at  0.50  of  the  stroke,  but  the  varying  degree  of  superheating 
prevents  any  conclusion  on  this  point.  Now  the  initial  con 
densation  of  moist  steam  interferes  with  the  gain  to  be  antici- 
pated from  large  expansion,  and  since  superheated  steam  re- 
duces the  initial  condensation,  it  might  be  expected  that  its 
use  would  permit  the  use  of  higher  degrees  of  expansion.  No 
experiments  can  be  quoted  that  are  conclusive  on  this  point. 

The  consumption  of  moist  steam  for  Experiment  D  is  much 
greater  than  that  for  either  Experiment  C  or  Experiment  E, 
and  it  is  noticeable  that  the  back  pressure  is  much  greater 
while  the  horse-power  is  less.  No  explanation  is  given  by  Ish- 


2$  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

erwood  of  these  facts,  though  he  includes  this  test  with  others 
in  his  comparisons,  in  which,  however,  he  makes  allowance  for 
differences  of  initial  pressure  and  back  pressure.  If  we  omit 
this  experiment,  the  consumption  of  moist  steam  per  horse- 
power per  hour  with  the  cut-off  at  half-stroke  was  32.7  pounds. 
The  mean  consumption  of  superheated  steam  for  Experiments 
G,  I,  L,  and  N  was  26.2  pounds.  The  gain  from  the  use  of 
superheated  steam  was  therefore 

32.7  —  26.2 

-  —  --  =  0.20  nearly. 

Taking  the  consumption  of  fuel  per  horse-power  per  hour 
as  the  basis  of  comparison,  the  real  gain  was 

2.87  —  2.40 

--  =ai6- 


Dixwell's  Tests.  —  The  Harris-Corliss  engine,  now  in  the 
laboratory  of  the  Institute  of  Technology,  was  fitted  up  by 
Mr.  George  B.  Dixwell  *  for  the  purpose  of  making  experi- 
ments on  superheated  steam.  At  his  request  a  board  of  three 
engineers  of  the  United  States  Navy  witnessed  a  series  of  ex- 
periments made  on  this  engine  in  1877  with  apparatus  belong- 
ing to  the  Institute. 

The  following  is  the  substance  of  the  report  made  by  the 
board,  of  which  C.  H.  Loring,  Chief  Engineer  U.  S.  N.,  was 
*  Jthe  senior  officer  : 

In  the  apparatus  employed  steam  was  taken  from  the  hori- 
zontal tubular  boilers  which  supplied  steam  for  heating  the 
buildings  of  the  Institute  of  Technology,  and  for  other  pur- 
poses. 

The  engine  is  of  a  well-known  Corliss  type,  of  S8  inches  diam- 
eter and  24  inches  stroke  of  piston.  The  cut-off  was  varied  by 
an  Allen  governor.  The  entire  clearance  is  yfj-g-  of  the  space- 
displacement  of  the  piston. 

*  Proceedings  of  the  Society  of  Arts,  M.  I.  T.     1887-88. 


TESTS   OF  SIMPLE   STEAM-ENGINES. 

The  power  developed  by  the  engine  was  absorbed  by  a  fric- 
tion-brake applied  to  the  fly-wheel. 

The  exhaust  steam  from  the  engine  passed  to  the  calorim- 
eter, which  comprised  the  following  details : 

1.  A  tank  built  of  planks  two  inches  thick,  of  about   120 
cubic  feet  capacity,  containing  a  system  of  tubular  metallic  con- 
densing surfaces,  the  interior  of  the  latter  being  in  communica- 
tion with  the  exhaust-pipe  of  the  engine  and  with  the  receiving- 
tanks  hereinafter  described.     The  body  of  the  tank  could  be 
filled  with  water  from  the  city  aqueduct,  by  which  heat  in  the 
steam  discharged  from  the  cylinder  into  the  system  of  condens- 
ing tubes  was  absorbed.     To  relieve  the  walls  of  the  tank  from 
pressure  resulting  from  the  expansion  of  the  water  in  heating,, 
a  small  vessel  of  ten  feet  cubical  capacity,  two  feet  high,  of 
wood,  was  placed  above  the  large  tank  described  above,  com- 
municating with  the  latter  by  a  pipe  of  two  inches  diameter. 
Through  this  pipe  the  expanding  water  could  rise  to  the  upper 
vessel  described,  which  is  called  the  expansion  tank.     The  es- 
cape of  vapor  was  prevented  by  a  floating  cover  in  the  expan- 
sion tank,  joined  to  the  walls  by  a  flexible  diaphragm.     The 
large  tank,  the  expansion  tank,  and  their  contents  and  appen- 
dages, stood  upon  the  platform  of  a  Fairbanks  scales.     Free- 
dom of  movement,  within  sufficiently  wide  limits,  was  main- 
tained by  fitting  the  pipe  connections  of  the  tank  with  rubber 
tubing ;  and  the  weighing  was  accurate  within  two  pounds ;  the 
whole   weight,    tanks,  appurtenances,    and   water   being   8100 
pounds. 

The  tank  was  fitted  with  thermometers  for  ascertaining  the 
temperature  of  the  hydrant  water  entering,  and  of  the  water 
contained.  To  insure  equality  of  the  latter  quantity  in  all 
parts  of  the  tank  chamber,  a  device  for  circulating  the  water 
was  provided,  to  be  worked  by  hand. 

The  fall  of  pressure  in  the  condenser  tubes,  below  that  of 
the  atmosphere,  was  averted  by  the  automatic  action  of  a  re- 
verse, or  vacuum,  valve. 

2.  The  pipe  leading  from  the  lower  end  of  the  condensing 
tubes,  through  which  the  water  resulting  from  condensation 


258  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

passed  out  'of  the  large  tank,  entered  a  small  tank,  which,  like 
the  others,  was  made  of  2-inch  plank.  This  tank  stood  upon 
the  platform  of  a  second  Fairbanks  scales,  and  was  fitted  with 
a  thermometer  for  ascertaining  the  temperature  of  its  contents. 
This  tank  could  be  emptied  through  a  pipe  leading  to  the 
sewer.  The  pipe  connections  were,  like  those  of  the  large 
tank,  flexible,  so  as  to  admit  of  weighing. 

The  superheating  apparatus  consisted  of  a  cylindrical 
boiler,  of  iron,  seven  feet  long  and  three  feet  in  diameter,  fitted 
with  fifty  iron  tubes  two  inches  in  diameter  and  five  feet  long. 
The  latter  were  fire  tubes,  vertical,  and  six  inches  of  the  lower 
end  covered  with  water.  The  superheater  was  set  in  brick- 
work, in  which  an  annular  space  allowed  the  products  of  com- 
bustion to  pass  downward,  around  a  part  of  the  shell.  The 
furnace  was  of  brickwork,  so  far  removed  from  the  heating 
surfaces  as  to  prevent  direct  radiation  to  them  from  the  fuel. 
In  this  vessel  the  steam  from  the  boiler  could  be  superheated 
above  600°  F. 

The  superheated  steam  was  delivered  to  the  engine  through 
a  2-J-inch  pipe.  At  the  receiving  end  of  this  pipe  a  pipe  of  \\ 
inches  diameter  delivered  saturated  steam,  the  admission  being 
regulated  so  as  to  govern  the  temperature  of  the  steam  passing 
through  the  pipe,  which  nevertheless  remained  superheated  to 
a  degree  measured  by  a  Bulkley  pyrometer,  placed  five  or  six 
feet  beyond. 

A  mercurial  thermometer  was  placed  close  to  the  steam- 
chest  of  the  engine,  in  the  steam-pipe,  and  another  Bulkley 
pyrometer  in  the  clearance  space  of  the  cylinder.  A  mercu- 
rial thermometer  was  also  placed  at  the  point  last  mentioned. 
During  a  part  of  the  experiments,  a  mercurial  high-grade  ther- 
mometer was  placed  nearly  midway  of  the  length  of  the  steam- 
pipe. 

Besides  the  pipes  described,  others  connecting  the  engine 
directly  with  the  generator  were  fitted.  These  were  cut  off 
from  the  former  at  will,  by  gate-valves  made  perfectly  tight- 

An  indicator  was  fitted  to  each  end  of  the  cylinder. 


TESTS  OF  SIMPLE   STEAM-ENGINES.  259 

The  experiments  were  made  in  pairs,  as  follows : 

1.  Saturated  steam,  \  cut-off;  followed  by  one  at  the  same 
cut-off  with  superheating. 

2.  Saturated  steam,  -^  cut-off ;  followed  by  one  at  the  same 
cut-off  with  superheating. 

3.  Saturated  steam,  \  cut-off;  followed  by  one  at  the  same 
cut-off  with  superheating. 

Diagrams  from  each  end  of  the  cylinder  were  taken,  and 
readings  from  the  pressure-gauge  and  thermometers,  and  of  the 
weighing  scales,  were  registered  every  five  minutes.  The  large 
tank  was  heated,  before  the  beginning  of  each  experiment,  to 
the  temperature  at  which  it  was  desired  to  close  the  experi- 
ment ;  then  emptied,  and  weighed  empty ;  then  filled  with 
water  from  the  city  aqueduct,  at  the  natural  temperature,  the 
temperature  observed,  and  the  full  tank  weighed.  Throughout 
each  experiment  the  water  in  the  tank  was  kept  in  motion,  that 
the  circulation  might  prevent  differences  in  temperature  within 
it.  The  temperature  and  weight  of  the  tank  water  at  the  end 
of  the  experiment  was  registered  after  clearing  the  condensing- 
tubes  of  water.  The  water  delivered  into  the  small  receiving- 
tank  was  also  weighed,  and  its  temperature  ascertained  every 
five  minutes.  From  these  quantities  the  total  heat  of  the  steam 
leaving  the  cylinder  is  computed. 

It  was  sought  to  maintain  in  the  cylinder,  during  each  ex- 
periment with  superheated  steam,  a  temperature  310°  F.,  and 
an  initial  pressure  of  50  pounds  by  the  gauge. 

It  will  be  seen  from  Table  IV,  page  261,  which  contains  the 
averages  of  all  the  observations  recorded,  that  this  was  very 
nearly  accomplished. 

It  will  also  be  seen  that  to  maintain  the  above  temperature 
within  the  cylinder  a  varied  degree  of  superheating  was  neces- 
sary, accordingly  as  the  cut-off  was  varied. 

After  the  experiments  were  completed,  the  correctness  of 
the  instruments  used  was  verified  by  the  very  accurate  methods 
of  the  Institute  of  Technology.  It  was  then  ascertained  that 
some  leakage  of  piston  and  valves  had  existed.  This  leakage 
affects  the  cost  of  the  power,  but  not  the  correctness  of  the  de- 


260  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

ductions  from  the  data  obtained,  in  their  bearings  upon  the 
object  of  the  experiments. 

Discussion  of  Results. — The  following  points  are  notice- 
able features  of  the  experiments,  and  of  the  action  of  the  ap- 
paratus : 

1.  Throughout  all  the  experiments  with  saturated  steam, 
considerable  variations  in  the  temperature  of  the  cylinder  were 
indicated  by  the  thermometer  and  the  pyrometer  during  every 
stroke  of  the  piston.     The  amplitude  of  the  vibrations  of  the 
pyrometer  extended   over  nineteen  degree-marks  of  the  dial. 
But  throughout  the  whole  of  every  stroke  of  the  piston,  during 
the  experiments  with   superheated  steam,   these   instruments 
constantly  indicated  a  fixed  degree  of  temperature,  showing  no 
vibrations  whatever. 

At  the  close  of  the  half-stroke  and  the  seven-tenths  stroke 
cut-off  experiments  with  superheated  steam,  the  same  instru- 
ments showing  no  vibrations,  the  cut-off  was  shortened  without 
change  in  the  superheating.  Vibrations  of  considerable  ampli- 
tude were  presently  observed  in  them. 

2.  The  remarkable  fall  of  temperature  of  the  steam  in  pass- 
ing from  the  superheater  to  the  steam-chest,  before  entering 
the  latter,  being  for  £  cut-off,  97°;  for  J  cut-off,  49°;  for  T7¥, 

19°. 

3.  During  experiments  with  superheated  steam  the  open- 
ing of  the  indicators  for  preliminary  heating  was  attended  by  a 
sudden  fall  of  15°  F.  within  the  cylinder,  the  temperature  gradu- 
ally rising  again  as  the  metal  of  the  indicators  became  heated. 

After  using  superheated  steam,  five  minutes  were  required 
for  a  fall  of  15°,  the  steam  being  shut  off. 

The  least  consumption  of  steam,  whether  moist  or  super- 
heated, was  found  with  the  cut-off  at  0.44  of  the  stroke.  The 
gain  in  steam  consumption  from  the  use  of  superheated  steam, 
with  about  140°  F.,  superheating,  was 

42.2  —  31.7 
——--  =  0.25  nearly; 

but  since  fuel  was  used  to  superheat  the  steam  the  real  gain 
was  not  so  great.     The  fuel  consumption  could  not  be  deter- 


TESTS  OF  SIMPLE  STEAM-ENGINES. 


26l 


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t^.  N   u-)\O    W   >0 

[NOTE.  —  The  above  temperatures  are  the  uncorrected  indications  of  the  instruments,  which,  tested  under  a  pressure  of  50  1 
indicated  as  follows:  Pyrom.  in  st.  pipe,  296;  Mid.  th.  300;  Thermom.  near  throttle,  303;  Cyl.  pyrom.  299;  Cyl.  th.  294  ;  Ex 
296.  —  G.  jS.  Z>.] 

•33JOJJS   JO 

pus  IB  japuijAo  ui 

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Pressure  in  cylinder  above  zero  shown  by  indicator. 

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262  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

mined  in  these  tests,  so  the  real  gain  may  be  estimated  as  fol- 
lows. The  steam  from  the  boiler  probably  contained  one  per 
cent  of  moisture,  so  that  each  pound  of  steam  may  be  assumed 
to  have  brought  to  the  cylinder  of  the  engine 

0.997-  +  ?  —  &!=  0.99  X  901.9  +  272.5  -  183.9  =  98i-5  B.  T.  U., 


in  which  r  and  q  are  the  latent  heat  and  heat  of  the  liquid  for 
the  temperature  of  303°  F.,  and  q^  is  the  heat  of  the  liquid  at 
15.65  pounds  pressure.  On  the  other  hand,  the  superheated 
steam  brought  in  per  pound 

CP(*»  —  0  +  A  —  £o  =  0.48(441  —  299.4)  +  1  173.2  —  182 

=  1059.2  B.T.  U., 

in  which  cp  is  the  specific  heat  of  superheated  steam  at  constant 
pressure,  and  /,  is  the  temperature  of  the  superheated  steam  in 
the  steam-pipe  near  the  throttle-valve  ;  /  is  the  temperature  of 
saturated  steam  at  the  pressure  in  the  steam-pipe,  and  A  is  the 
total  heat  of  steam  at  that  temperature  and  pressure  ;  while  qQ 
is  the  heat  of  the  liquid  at  the  pressure  of  the  back  pressure. 
There  appears  to  be  a  discrepancy  between  the  boiler-pressure 
and  the  initial  indicated  pressure  in  each  experiment,  so  that 
the  initial  pressure  in  the  cylinder  has  been  taken  in  this  calcu- 
lation. 

The  number  of  thermal  units  per  horse-power  per  hour  fur- 
nished to  the  engine  in  the  test  with  saturated  steam  was 

42.2  X  981.5  =  41420, 
while  with  superheated  steam  the  number  of  thermal  units  was 

31.7  x  1059.2  =  3358, 
and  the  gain  from  the  use  of  superheated  steam  was 

41420-33580 
41420 

In  the  experiments   made  with   saturated  steam  the  per 
cent  of  water  at  cut-off  decreased  rapidly  as  the  cut-off  was 


TESTS  OF  SIMPLE   STEAM-ENGINES.  263 

lengthened,  and  the  per  cent  of  water  at  release  also  decreased, 
though  much  less  rapidly. 

In  the  experiments  made  with  superheated  steam,  Experi- 
ment 5  shows  the  same  per  cent  of  water  at  cut-off  and  at  re- 
lease, which  indicates  that  the  condensation  and  re-evaporation 
during  expansion  were  equivalent.  Experiment  4  shows  re- 
evaporation  during  expansion,  and  Experiment  6  shows  con- 
densation during  expansion. 

By  aid  of  the  last  column  of  Table  IV  the  per  cent  of  mois- 
ture in  the  exhaust  steam  may  be  calculated  as  follows :  The 
mean  back  pressure  is  15.35  pounds,  at  which  the  heat  of  vapo- 
rization 13964.4  and  the  heat  of  the  liquid  is  183,  so  that  if  x  is 
the  part  of  the  mixture  that  is  steam, 

964.4^  +  183  =  1046; 

.-.  x  =  0.895, 

and  the  per  cent  of  moisture  is  10.5. 

The  other  experiments  with  saturated  steam  show  a  less 
degree  of  moisture.  The  experiments  with  superheated  steam 
show  that  the  exhaust  steam  was  superheated  in  the  two  last 
experiments,  and  that  it  was  moist  in  Experiment  4. 

Automatic  Cut-off  Engines. — At  the  First  Millers'  Inter- 
national Exhibition  at  Cincinnati,  June  1880,  some  competi- 
tive tests  were  made  by  John  W.  Hill  on  three  automatic  cut^ 
off-engines,  condensing  and  non-condensing,  the  results  of 
which  are  of  interest  since  they  show  the  performance  of  well- 
made  unjacketed  simple  engines. 

Two  of  the  engines  were  modified  forms  of  the  well-known 
Corliss  engine,  known  as  the  Reynolds-Corliss  and  the  Harris- 
Corliss  engines.  The  third  engine  made  by  Wheelock  had 
two  semi-rotative  valves  similar  to  the  Corliss  valve,  one  at 
each  end  of  the  cylinder  to  give  admission  and  exhaust  of 
steam,  and  also  two  cut-off  valves  of  similar  form,  which  cut  off 
the  supply  of  steam  to  the  main  valve.  It  had  consequently 
two  clearances,  one  for  compression,  and  a  larger  one,  including 
the  space  between  the  two  valves,  for  expansion. 

The  dimensions  of  the  engines  were  as  follows : 


264  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

DIMENSIONS   OF    ENGINES. 


Reynolds- 
Corliss. 

Harris- 
Corliss. 

Wheelock. 

Diameter  of  cylinder,  inches  

18  02 

18  03 

18  26 

2  68 

"          "  steam-pipe,  inches  

6 

"          "  exhaust-pipe,  inches  
"          "  fly-wheel  feet      

x76 

8 
16 

8 
16 

Area  steam-ports,  square  inches  

Area  exhaust-ports     "          "      .... 

Stroke  of  piston  ,  inches  

48 

48 

48 

Weight  of  engine,  exclusive  of  fly-wheel, 

Weight  of  fly-wheel,  pounds  

Clearance  in  decimal  of  stroke 

Release  in  decimal  of  stroke,  condensing.. 
"  non-condensing. 
Exhaust  closure  in  decimal  of  stroke,  con- 
densing           

0.978 
0.981 

0.940 
0.969 

0.956 
0.970 

0.056 

Exhaust  closure  in  decimal  of  stroke,  non- 

o  084 

Diameter  air-pump  cylinder  inches.  .  .  . 

o  81 

Diameter  overflow-pipe,  inches  

6 

•3.  e 

Stroke  of  air-pump  piston  inches 

The  Wheelock  engine  had  a  Bulkley  condenser  with  the 
head  of  the  condenser  set  34  or  35  feet  above  the  level  of  the 
hot-well  so  that  no  air-pump  was  required. 

The  feed-water  supplied  to  the  boilers  furnishing  steam  for 
the  tests  was  weighed  in  a  tank  on  scales.  The  quality  of  the 
steam  was  determined  by  a  continuous  calorimeter.  The  con- 
densing water  was  measured  by  a  water-meter,  and  though  the 
quantities  thus  determined  are  introduced  in  the  tables  they 
cannot  be  taken  with  full  confidence. 

The  steam-pressure  in  the  boiler  and  in  the  steam-pipe,  and 
the  vacuum  in  the  condenser,  were  taken  with  gauges.  The 
pressure  of  the  atmosphere  was  taken  with  an  aneroid  ba- 
rometer. 

All  temperatures  were  taken  with  mercurial  thermometers. 

Diagrams  were  taken  every  fifteen  minutes  with  Thomp- 
son indicators  at  each  end  of  the  cylinder,  and  all  other  obser- 
vations were  read  at  the  same  intervals. 

The  work  of  the  engines  was  applied  to  drive  rotary 
pumps.  Attempts  were  made  to  find  the  friction  of  the  en- 
gines, and  tests  of  regulation  at  various  loads  were  also  made. 

The  summary  of  the  results  of  tests  are  given  in  Table  V : 


TESTS  OF  SIMPLE   STEAM-ENGINES. 


265 


TABLE   V. 
AUTOMATIC  CUT-OFF  ENGINE. 


Condensing. 

Non  -condensing. 

Rey- 
nolds- 
Corliss. 

Harris- 
Corliss. 

Whee- 
lock. 

Rey- 
nolds- 
Torliss. 

Harris- 
Corliss. 

Whee- 
lock. 

10 

95.8 

92.5 
29.72 
25-45 

84°.  2 

72.4 

ibi  .  7 
75-4 
59-  J 

QI.I 

0.124 

86.3 
•15-2 
4-5 
13-6 
35-4 

162.3 
10.6 
6.1 

utt 

0.879 

1427.5 

68.92 

77°  -°3 
131°.  96 
107°.  42 
1243-8 

10 
96.1 

91.7 

29-55 
25.67 
87°.  6 
75-9 
97-5 
75-8 
75-8 

0°119 

87.0 
14.6 

4:1 

35-7 

165.6 
9.6 

6.2 

1454.!7 

0.876 

J405  7 
5°  -55 
78°.  07 

121°.  87 

97°.  86 
x3i5-9 

10 

96.3 

91.4 
29.41 
23.98 
83°-  3 
77-2 
111.7 
74-5 

4-« 

92-5 
29.75 

87°  '4 

75-3 

10 

96.3 

91-5 
29-55 

85°'.3 
75-8 

10 

96.3 

9i-5 
29.48 

78°  '.8 
70!  i 

Barometer                                       inches  hg" 

'*            of  injection  " 

air-pump  
DIAGRAMS. 

88.1 
0.131 

77-7 
14.0 

£.1 

33-9 

158.4 
7.8 
6.0 
*o.6 
143.9 
0.909 

1797-5 
69.20 
77°.  24 
123°.  25 
io6°.57 
1301.7 
o  080 

90.0 
0.160 

84.8 
17.4 
0.9 
34-7 
29.8 

i37-o 
10.3 

5-i 

121.  "7 

0.886 

1303-9 
68.33 
76°.  86 
i34°.  86 
104°.  45 
1211.3 

89.5 
0.136 

85-9 
17.0 
0.4 
46.1 
28.9 

134-3 
9.6 
5-o 

119  "7 

0.892 

1530-9 
54-77 
77°.  87 
119°.  27 
980.67 
1255-7 

88.5 
0.170 

76.9 
17-5 

I.O 

44-2 
29.4 

140.0 
8.0 
5-3 

126."7 

0.905 

1836.3 
67.70 
76°-  45 
120°.  85 
io8°.74 
1313-1 

Cut-off  in  decimal  of  stroke  

Maximum  compression  pressure.... 

LOADS. 

Extra  friction  due  to  load,  estimated  

Coefficient  of  useful  effect       

CALORIMETER. 
Condensing-water  per  hour  pounds 

Temperature  of  injection  Fahr. 

"  overflow  " 

41              "  condensation  " 

Thermal  value  of  steam  B.  T.  U. 
Relative  value  of  steam  

STEAM  EXPENDED. 

34425 

32296 

31538 

32645 

32708 

35749 

Leakage  of  tanks               

29-5 
—  142.8 
620.025 
33606 

20.6 

23-5 

19-5 

14.9 

103783 
30-9 

+285  '-7 
505-500 
32063 

19.4 

22.1 

19.4 

13-8 

104307 
32-5 

692.000 
30847 

19.5 

21.4 

19-3 

13-9 

76324 
24-7 

15-75 

615.000 
31994 

25.9 

29.2 

23-9 
19.0 

547-750 
32160 

23.9 

26.8 

22.1 

18.0 

-214.3 

645  .  750 
34889 

24.9 

27-5 

24-9 
19.8 

Correction  for  variation  of  water-level  

Net  steam  delivered  to  engine  
ECONOMY  OF  ENGINE. 
Steam  per  indicated  horse-power  per  hour 
actual                                        .... 

Steam  per  net  horse-power  per  hour  actual 
Steam  per  indicated  horse-power  per  hour 
corrected  for  relative  value  of  steam.  . 

CALCULATED  ECONOMY. 
Steam  per  horse-power  per  hour  by  the  dia 
grams  

CONDENSING  WATER. 
Water  expended  per  hour  
Water  expended  per  pound  of  steam  

.... 

*  Power  required  to  raise  water  for  condenser. 


266  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Hoadley  Portable  Engine. — The  following  are  the  data 
and  results  of  a  test  on  a  Hoadley  portable  steam-engine, 
made  at  the  International  Exhibition,  at  Philadelphia,  1876. 
The  engine  was  a  simple  single-cylinder  engine,  lagged  but  not 
jacketed,  with  a  piston  slide-valve  controlled  by  an  automatic 
governor,  and  mounted  on  the  top  of  an  unclothed  locomo- 
tive boiler.  The  coal  was  anthracite  of  ordinary  quality,  used 
without  drying. 

TEST  OF  A  HOADLEY  PORTABLE  ENGINE. 

Diameter  of  cylinder, 14. 56  in. 

"         "  piston-rod, 2.375  " 

Length  of  stroke, 1.66  ft. 

Clearance,  fraction  of  piston  displacement :  crank  end,     .  0.077 

head  end,       .  0.157 

Duration  of  test, 6  hrs.  2  rain. 

Revolutions  per  minute, 125.96 

Steam-pressure  in  boiler, I2O  Ibs. 

Initial  pressure  :  crank  end, 124.75 

head  end, HQ-9 

Absolute  pressure  at  end  of  stroke  :  crank  end,    ....  23.4 

head  end,     ....  31.9 

Absolute  pressure  at  admission  :  crank  end, 112.5 

head  end, H7-7 

Mean  absolute  forward  pressure  :  crank  end, 58.4 

head  end,    .          ...  69.2 

Mean  absolute  back  pressure  :  crank  end,  .     .          ...  24.7 

head  end, 25.9 

Mean  effective  pressure  :  crank  end, 33.7 

head  end, 43.3 

Point  of  cut-off  :  crank  end, O-I43Q 

head  end, 0.2091 

Indicated  horse-power  :  crank  end, 34.6 

head  end, 45-69 

Total, ~     '.  80.29 

Horse-power  by  brake, 72.72 

Friction  of  engine,  horse-power, 7.57 

Horse-power  by  indicator  without  load 5.80 

Steam  per  I.  H.  P.  per  hour,  weighed 25.61  Ibs. 

"        "    brake  H.  P.  per  hour,  weighed 28.27    " 

"    I.  H.  P.  per  hour,  indicator, 19-38     " 

"         "    brake  H.  P.  per  hour,  indicator, 21.4      " 

Coal  per  indicated  horse-power  per  hour, 3.35      " 

"      "    brake  "  "      "         3.69      " 


TESTS  OF  SIMPLE   STEAM  ENGINES.  267 

Heating  surface  of  boiler, 461.5  sq.  ft. 

Area  of  grate, 12.75       " 

Coal  per  sq.  ft.  per  hour, 21.07  Ibs. 

Water  evaporated  per  sq.  ft.  per  hour,  heating  surface,     .  4.46     " 

Ratio  of  ashes  to  coal  burned, 0.118 

Water  evaporated  per  pound  of  coal, 7.65  Ibs. 

"  "        "      "  combustible, 8.68    " 


V      CHAPTER   XVI. 

TESTS  OF   SIMPLE  AND   COMPOUND   ENGINES. 

THE  several  series  of  tests  following  give  the  data  for  the 
comparison  of  the  performance  of  simple  and  compound  engines. 
All  the  tests  except  those  on  the  Gleam  were  made  by  engi- 
neers of  the  United  States  Navy  and  the  United  States  Rev- 
enue Marine,  and  consist  of  tests  on  the  coast-survey  steamer 
Bache ;  of  tests  on  the  revenue  steamers  Rush,  Dexter,  and 
Dallas ;  and  of  tests  on  the  revenue  steamer  Gallatin  ;  also  of 
tests  on  the  Herreshoff  steam-yachts  Leila,  Siesta,  and  on  the 
yacht  Gleam. 

The  principal  dimensions  of  the  engines  and  boilers  of  the 
United  States  steamers  are  given  in  the  following  table : 

DIMENSIONS  OF  ENGINES  AND  BOILERS. 


Bache. 

Rush. 

Dexter. 

Dallas. 

Gallatin. 

Diameter  of  cylinders,  ins.,  high  pressure 

"             "     low 

15.98 
25 

3 

26"" 

'36'" 

34-i 

*«          "              "           "     iow      " 

06 

Clearance  per  cent,  high  pressure  

4.86 

7.887 

"          low         "       

5.849 

8  02 

Grate  surface  square  feet     

57 

57 

1689  24 

Tests  on  the  Bache. — The  engine  and  hull  of  the  United 
States  coast-survey  steamer  Bache  were  built  in  1870  from 
designs  by  Mr.  Emery,*  then  consulting  engineer  to  that  de- 
partment. The  engine  is  a  direct-acting,  inverted,  compound 
engine,  with  the  small  cylinder  above  the  large  cylinder,  both 
pistons  being  attached  to  one  piston-rod.  The  small  cylinder 


*  Journal  Franklin  Institute,  May,  1875. 


268 


TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES.          269 

was  not  jacketed,  but  the  large  cylinder  had  a  steam-jacket  on 
the  sides  and  ends ;  when  working  compound  the  steam  for 
the  jacket  was  taken  from  the  bottom  of  the  small  steam-chest ; 
when  working  as  a  simple  engine,  with  the  small  cylinder  dis- 
connected, the  steam  was  taken  from  the  main  steam-pipe. 
Suitable  pipes  and  valves  were  provided  so  that  steam  could  be 
supplied  directly  to  the  large  cylinder,  and  excluded  from  the 
small  cylinder,  in  which  case  the  large  cylinder  acted  as  a  sim- 
ple expansive  engine.  Ordinarily  the  steam  passed  from  the 
small  to  the  large  cylinder  through  a  large  pipe  which  acted  as 
intermediate  receiver.  Both  cylinders  were  provided  with  short 
slide-valves  and  independent  cut-off  valves  on  the  back  of  the 
main  valves,  and  the  valves  of  both  cylinders  were  actuated  by 
continuous  valve-stems.  The  engine  had  a  surface  condenser. 
The  air-pump  was  operated  by  levers  from  the  main  cross-head. 
The  circulating  pump  was  of  the  centrifugal  pattern,  driven  by 
an  independent  engine. 

During  the  trials  the  vessel  was  secured  to  the  dock. 

The  feed-water  was  measured  in  a  tank  with  two  compart- 
ments that  were  filled  and  emptied  alternately.  The  capacity 
of  each  compartment  was  ascertained  by  weighing  water  into 
it,  of  the  average  temperature  of  the  feed-water.  Indicator- 
diagrams  were  taken  every  twenty  minutes. 

The  water-level  in  the  boiler  was  noted  every  time  the 
feed-water  tank  was  filled,  but  it  did  not  vary  appreciably. 
The  condensed  water  from  the  jackets  and  receiver  was  col- 
lected and  weighed  separately  and  returned  to  the  feed-water 
tank.  . 

In  the  ninth  experiment  the  coal  was  weighed,  but  in  the 
others,  which  were  shorter  in  duration  the  water  only  was 
weighed.  The  coal  used  was  anthracite  of  fair  quality. 

The  data  and  results  of  the  experiments  are  given  in 
Table  VI. 

Tests  on  the  Rush,  Dexter,  and  Dallas. — In  1874  three 
vessels  were  built  for  the  United  States  Revenue  Marine, 
which  were  designedly  alike  in  all  respects,  except  that  the 
engines  were  of  three  distinct  types,  and  the  boilers  were 


270 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


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TESTS   OF  SIMPLE  AND    COMPOUND  ENGINES.          2JI 

adapted  to  the  engines.  The  Rusk  had  a  direct-acting,  in- 
verted, compound,  receiver  engine,  with  the  cranks  90°,  thor- 
oughly steam-jacketed,  felted,  and  lagged,  designed  to  use 
steam  at  80  pounds  pressure.  The  small  cylinder  had  an  inde- 
pendent cut-off  valve  on  the  back  of  the  main  valve ;  the  large 
cylinder  had  a  double-ported  valve  arranged  to  cut  off  at  about 
half-stroke. 

The  Dexter  had  a  single-cylinder,  direct-acting,  inverted  en- 
gine, felted  and  lagged,  but  not  steam-jacketed.  The  cut-off 
could  be  varied  by  adjustable  cut-off  plates  on  the  back  of  the 
main  valve.  The  steam-pressure  was  intended  to  be  70 
pounds. 

The  engine  of  the  Dallas  was  also  a  single-cylinder,  in- 
verted engine,  but  was  intended  to  carry  a  steam-pressure  of 
40  pounds.  The  cylinder  was  covered  with  a  non-conducting 
composition  and  lagged,  but  not  steam-jacketed.  Steam  was 
distributed  by  a  slide-valve  with  adjustable  cut-off  plates  on  the 
back. 

The  experiments  were  made  under  the  direction  of  Chief 
Engineer  C.  H.  Loring,  U.  S.  N.,  and  Chas.  E.  Emery,*  Con- 
sulting Engineer  U.  S.  R.  M.,  assisted  by  two  chief-engineers 
of  the  navy  and  two  of  the  revenue  marine,  with  a  sufficient 
force  of  assistants  and  helpers. 

During  the  experiments  the  vessels  were  secured  to  the 
dock. 

The  coal,  which  was  anthracite  of  fair  quality,  was  sent 
from  the  dock  in  bags,  filled  to  a  certain  weight,  as  wanted. 
The  ashes  were  measured  in  buckets  and  then  weighed  in 
gross  on  the  wharf.  One  experiment  on  each  engine  was  of 
sufficient  length  to  determine  the  evaporative  efficiency  with 
certainty.  The  other  experiments  were  shorter,  and  for  them 
the  consumption  of  water  only  was  determined. 

The  feed-water  was  measured  in  a  tank  with  two  compart- 
ments, which  were  alternately  filled  and  emptied,  as  it  came 
from  the  condenser  and  passed  to  the  boiler.  The  waste  from 

*  Journal  Franklin  Institute,  I,  .ay,  18751 


272  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

leakage,  etc.,  was  supplied  from  a  hydrant  and  charged  in  the 
cost. 

A  number  of  indicators  were  compared  under  steam-pres- 
sure with  a  standard  gauge,  and  a  pair  selected  that  were  cor- 
rect at  varying  pressures.  Diagrams  were  taken  every  twenty 
minutes. 

The  data  and  results  are  given  in  Table  VII. 

Tests  on  the  Gallatin. —  The  United  States  revenue 
steamer  Gallatin,  built  in  1870,  was  re-engined  in  1874  accord- 
ing to  designs  of  Mr.  Charles  E.  Emery,  and  tested  by  Chas. 
H.  Loring,  U.  S.  N.,  and  Mr.  Emery*  at  the  Boston  Navy 
Yard  in  Dec.  1874  and  Jan.  1875. 

The  Gallatin  had  a  single,  inverted,  steam-jacketed,  direct- 
acting  engine,  with  a  slide-valve  set  to  cut  off  at  two-thirds 
stroke,  and  an  adjustable  cut-off  valve  on  the  back  of  the  main 
valve.  The  air-pump  was  operated  by  levers  from  the  main 
cross-head.  The  cooling  water  for  the  surface  condenser  was 
supplied  by  a  centrifugal  pump  driven  by  an  independent  en- 
gine. The  boiler,  steam-pipes,  and  cylinder  were  covered 
with  hair-felt  and  canvas,  and  in  the  engine-room  the  exposed 
parts  were  covered  with  Russia  iron  or  wood  lagging. 

Steam  for  the  jackets  was  ordinarily  conducted  through  a 
felted  pipe  from  the  bottom  of  the  valve-chest  to  the  upper 
part  of  the  cavity  in  the  cylinder  cover.  A  second  pipe  leads 
from  the  bottom  of  the  cavity  in  the  cover,  upward  and  around 
to  the  side  jacket,  which  is  in  common  with  the  jacket  for  the 
bottom  of  the  cylinder.  Thus  any  water  which  collects  in  the 
bottom  of  the  valve-chest  or  cylinder  cover  is  carried  into  the 
main  jacket,  from  which  all  water  is  blown  into  the  hot-well 
through  an  intermediate  vessel  provided  with  a  glass  gauge. 

The  boiler  was  designed  to  carry  a  steam-pressure  of  60 
pounds ;  during  the  tests  it  was  worked  at  70  pounds  part  of 
the  time,  to  compare  with  tests  on  the  other  engines. 

The  experiments  were  made  with  the  vessel  secured  to  the 
wharf. 

*  Report  of  trial. 


TESTS  OF  SIMPLE   AND    COMPOUND  ENGINES. 


273 


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2/4  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  coal,  which  was  anthracite  of  fair  quality,  was  weighed 
in  bags  on  the  wharf  and  sent  on  board  as  needed.  The  ashes 
were  hoisted  in  buckets  and  weighed  in  bulk  on  the  wharf. 

The  condensed  steam  from  the  surface  condenser  was 
measured  in  the  tank  with  two  partitions,  which  was  used  in 
the  tests  on  the  revenue  steamers  already  described.  The 
water  from  the  jackets  was  cooled  by  passing  it  through  a  coil 
in  a  ship's  distiller,  and  then  weighed  in  an  open  tank.  After 
the  water  was  weighed  it  was  delivered  to  the  condenser,  and 
thus  was  charged  in  determining  the  cost  of  power. 

The  indicator-diagrams  were  taken  every  twenty  minutes. 

To  ascertain  the  evaporative  efficiency  of  the  boiler  the 
machinery  was  operated  continuously  for  48  hours  with  the 
steam-pressure  at  70  pounds. 

In  all  cases  when  the  steam-jacket  was  not  in  use,  a  joint  in 
the  pipes  was  broken  to  let  in  air  and  to  detect  leakage  of 
steam  into  the  jackets. 

In  working  out  the  results  some  of  the  experiments  dis- 
covered discrepancies,  and  when  errors  in  observations  were  de- 
tected such  experiments  were  rejected  ;  but  when  no  errors 
were  found  the  tests  were  reported  with  the  others,  though  all 
such  unsatisfactory  tests  were  made  in  the  first  of  the  work, 
before  the  observers  were  familiar  with  the  work.  In  the  tests 
numbered  13,  30,  34,  37,  40,  41,  and  42,  distinguished  by  an 
asterisk  in  the  table,  some  of  the  indicator-diagrams  were  faulty, 
and  were  corrected  by  comparison  with  diagrams  taken  under 
like  circumstances. 

Discussion  of  Results. — From  the  data  and  results  given 

in    Tables  VI,  VII,  and  VIII  may  be   found  the  advantage 

'  of  the  use  of  compound  engines,  of  the  use  of  steam-jackets, 

and    of    the    use    of    high-pressure    instead    of    low-pressure 

steam. 

In  order  to  make  the  comparison  more  readily  the  follow- 
ing table  is  given,  in  which  are  collected  some  of  the  data  and 
results  of  those  tests  that  gave  the  best  efficiency  under  differ- 
ent conditions. 


TESTS  OF  SIMPLE  AND    COMPOUND   ENGINES. 


275 


SIMPLE  AND  COMPOUND  ENGINES. 


i    4> 

V 

M 

o3  c 

Jj 

Lj 

-     .£ 

Name  of  engine. 

Method  of  working. 

£•& 

1 

Revolutio 
per  minute 

Total  numt 
of  expansic 

11 

If! 

Hi 

Bache 

Compound  with  jacket. 

80.2 

3.3 

53.2 

7.0 

99.2 

2O.3 

2I7OO 

Rush  '..'.'.'.. 

'        without    " 
with      "      .       . 

80.3 
69.1 

3-4 
3.5 

47-7 
70.8 

6-7 

6.2 

69.8 
266.5 

23.0 

18.4 

24500 
19600 

Bache 

Simple  with  jacket  

79-5 

3-7 

247OO 

Dexter 

without   '     

78.1 
68.7 

4.4 

47.1 
•56.15 

5-3 

89.2 
185  9 

26.2 

27600 
254OO 

Gallatin 

with        '     

61  i 

306    2 

without   '     

68.5 
95-8 

3-9 

59-9 

4-9 
6  8 

279.6 

162  3 

21-9 

23200 

In  the  group  of  tests  on  the  Gallatin  with  the  steam-jacket 
in  use  and  with  about  70  pounds  boiler-pressure,  there  are 
three  that  have  nearly  the  same  consumption,  and  of  these  the 
one  was  chosen  which  had  nearly  the  same  number  of  expan- 
sions as  the  other  tests  in  the  above  table,  and  with  which  it 
should  be  compared.  The  test  on  the  Reynolds-Corliss  engine 
was  included  in  the  same  table,  since  it  is  instructive  to  com- 
pare it  with  the  tests  on  marine  engines. 

Direct  comparison  of  the  consumption  of  steam  per  horse- 
power per  hour  of  the  tests  given  in  the  table  is  liable  to  be 
misleading,  on  account  of  the  difference  in  boiler-pressure  and 
back  pressure.  The  estimated  number  of  thermal  units  per 
horse-power  per  hour  has  been  calculated,  on  the  assumption 
that  the  steam  in  the  boiler  is  dry  and  saturated,  by  the  ex- 
pression 


in  which  A  is  the  total  heat  at  the  boiler-pressure  and  qQ  is  the 
heat  of  the  liquid  at  the  back  pressure.  The  back  pressure  is 
chosen  instead  of  the  pressure  in  the  condenser,  since  the  effi- 
ciency of  the  fluid  is  to  be  considered  rather  than  the  efficiency 
of  the  engines. 

The  least  consumption  of  steam  is  shown  by  the  engine  of 
the  Rush,  working  compound  with  both  cylinders  thoroughly 
steam-jacketed.  This  test  may  properly  be  compared  with 
the  test  on  the  engine  of  the  Gallatin,  working  single,  and 


2/6 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


TABLE  VIII. 
TESTS  ON  THE  GALLATIN. 


1 
2 

3 
4 
5 
6 

Description  of  Test. 

Dura- 
tion, 
hours. 

Cut-off 
raction 
of 
stroke. 

Ratio 
of 
ex- 
pan- 
sion. 

Temperatures, 
Fahrenheit. 

Ex- 
ter- 
nal 
air. 

En- 
gine- 
room. 

Sea- 
wat'r. 

>  Steam-jacket  not  in 

j-  Steam-jacket  in  use 
I  Steam-jacket  suppli 

use  • 

i  .9166 
2.25 

2.  I 

2-1333 
2.  2l66 
2  .2 

0.463 
0.640 
0.468 
0.648 
0.525 
0.626 

2.  O2 

I-5I 
2.OO 
1.49 
I.  80 

i-54 

36 
38 
36 
38-7 
25 
26 

64 
7°-5 
736 
69.7 
87.0 
7i-3 

35 
35 

i 

32 
32 

ed  with  steam  at  70  j 

• 

7 
8 
9 
10 
11 
12 
13* 

Steam-jacket  not  in 
use. 

Throttled             . 

1.7666 

I-9833 
2.05 
2.  I 
2.3166 
2.1667 
2.5666 

0.114 
0.139 
0.220 
0.271 
0.326 
0.413 
0.691 

5-92 

5-21 

3-73 
3-i6 
2.72 
2.23 
1.41 

i, 

41.  i 
40-3 
41.8 
36 

70 
70 
70 
62 
64.1 
64 
73-3 

1 

36-5 
36-9 

L7.s 

35 

14 
15 
16 
17 

18 
19 
20 
21 

Steam-jacket  in  use. 

2.Ol66 
2-05 
2.2 
2.21666 
2.0333 

3-75 
2.0833 
2.3 

0.105 
0.144 
0.155 
0.172 
0.221 
0  255 
0.378 
0.416 

6.08 
5-07 
4.82 
4-49 
3-71 
3-32 
2.40 

2.21 

19.7 
!3-3 
J9 
13 

22 
30.8 
40.9 
41 

69.5 
80 

74 
75-5 
76  5 
69.9 

65-9 
72-3 

34-4 
33 
35 
33 
34-7 
36.2- 
34 
34 

22 
23 
24 
25 

26 
27 

28 

Condensing  without 
vacuum. 

Steam-jacket  not    j 
in  use. 
Steam-jacket  in     J 
use.                j 

2.2 

2.21666 
2.05 
2.II66 

0.178 
0.240 
0.196 
0.237 

4-37 
3.48 
4.07 
3-52 

45 
39-5 
40.4 
36 

77-3 
76 
74-4 
74-6 

37 
34 

Link  hauled  up. 

Without  jacket  and  I 
ind.  cut  off.         f 

I  .91666 
2.06667 

I'9S 

0.366 
0.243 
0.383 

2-47 
3-45 
2-37 

4 
28.3 
14-3 

65 
71.7 
S6 

33 
32 
33 

With     | 
With        cut-off,   f 

jaCKCC-     Without/ 
cut-off.    ) 

29 
30 
31 
32 

>  Jacket  not  in  use. 
j-  Jacket  supplied  with  steam  from  boiler,  j 

2-5 

2.05 

1.8666 
2.0333 

0.151 
0  200 
0.153 
0.212 

4.91 
4.01 
4.87 
3-83 

40.4 
37-6 

6.6 

64.4 
63-3 
75-6 
74 

33-6 
34 
33-4 
32-5 

33 
34* 
35 
86 
37* 

Steam-jacket  not  in  use. 

23-95 
2.18333 
2.05 
2.0166 
1-9833 

0.173 
0.071 
0.123 
0.150 
0.185 

4.46 
7.78 
5-63 
4-94 
4-25 

20.9 
39-8 
46 
44-3 
36 

74-6 

67-5 
73-7 
72.3 
66 

34-5 
36 
36 

Il6 

38 
39 
40* 
41* 
42* 
43 

Steam-jacket  in  use. 

23-9833 
2.2166 
2.0166 
2.1166 
4.41666 
1-9333 

0.171 
0.080 
0.122 
0.148 
0.173 
0.189 

4-5° 

III 

:t 

4.19 

37-8 
43 
57-5 
32-5 
48.6 
39-5 

69.4 
70 
65 
43-3 
66.4 

75 

36 
36 
35-5 

II 

35 

TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES. 
TABLE  VIII.— Continued. 


2/7 


Temperatures, 
Fahrenheit. 

Pressures  —  pounds  per  square  inch. 

Dis- 

ch'rge 

w'ter. 

Hot- 
well. 

Feed- 
water 
in 

tanks. 

Boiler 
pres- 
sure by 
gauge. 

Vacu- 
um in 
con- 
denser, 
ins.  of 
mer- 
cury. 

Baro- 
meter 

Initial 
jressu'e 
abso- 
lute. 

Ter- 
minal 
pres- 
sure 
abso- 
lute. 

Cush- 
ion 
pres- 
sure 
abso- 
lute. 

Back 
pres- 
sure 
abso- 
lute. 

Vacu- 
um at 
half- 
stroke 

Mean 
effec- 
tive 
pres- 
sure. 

1 

75 

116.6 

"5-7 

14.56 

25-54 

14.8 

25-3 

ii.  i 

8-7 

3-7 

11.7 

15-8 

2 

80.25 

124.8 

121.  8 

12  83 

25 

14-8 

23-7 

I3-  T 

9-4 

3-8 

"•5 

16.1 

3 

84 

118.4 

"9-3 

15  42 

25.12 

14.7 

26.3 

12.0 

9.6 

3-6 

"•5 

16.8 

4 

78.3 

123 

I23-3 

13.14 

24.88 

14.8 

24.1 

13.8 

9-5 

4.0 

II.  2 

16.8 

5 

56-5 

iiS-5 

103.7 

13.39 

26.04 

15.0 

23-9 

9.2 

3-o 

12.5 

15-9 

6 

56 

"3-7 

112.3 

13.86 

*5-5 

15-0 

25.0 

14.2 

II.  0 

3-5 

12.0 

17.7 

7 

85 

"5 

103-7 

44.8 

25-9 

14.8 

56-3 

IO.2 

8.0 

3-3 

ii.  8 

20.8 

8 

65 

102.5 

100.7 

40  9 

26.1 

14.8 

52.8 

10.6 

8.0 

3-4 

11.7 

21.0 

9 

69-7 

111.7 

107.6 

43.3 

25-9 

14-8 

55-8 

13.2 

8.4 

3-2 

11.9 

26.2 

10 

88.8 

128.4 

132.4 

39.4 

23-6 

14.8 

51-8 

14.0 

10.8 

4-4 

10.  0 

26.5 

11 

72 

in.  i 

108 

39.5 

25-9 

14-8 

52-3 

16.4 

8-3 

3-7 

ii.  8 

30.8 

12 

106 

M7-5 

138.9 

37.67 

22.7 

14-8 

50-3 

19-3 

13.5 

5-5 

10.4 

3°-9 

13* 

79-3 

130.0 

122.8 

39.0 

24.6 

14.6 

44-7 

21.7 

8-3 

3-° 

11.7 

30-4 

14 

61.7 

98-3 

102-5 

45.4 

26.1 

14.8 

58.0 

9-8 

8-5 

3-7 

"•3 

19.9 

15 

60.7 

112 

109.7 

42.8 

26.5 

15.1 

53-9 

10.4 

11.4 

3-4 

ii.  i 

21.7 

16 

77 

109.6 

106.9 

41.6 

25-6 

14.8 

54-6 

10.3 

8.7 

3-5 

ii.  6 

21.7 

17 

61.5 

"5-5 

no.  2 

43  9 

26.6 

15-  1 

54-7 

"•5 

12.2 

3-8 

12.0 

23.6 

18 

80 

"5 

113.8 

41.3 

25-8 

14.8 

54-7 

11.7 

9.8 

3-8 

"•5 

24.6 

19 

96.7 

129.4 

123.6 

40.0 

24.6 

14.8 

52-4 

13-5 

II.4 

4-7 

10.7 

26.4 

20 

74-4 

in.  i 

105.8 

36.2 

26.4 

14.8 

49-3 

14.8 

I4.8 

2-9 

"•5 

28.5 

21 

85 

130 

123-5 

37.4 

24.8 

14.8 

50-4 

18.9 

10.6 

4-5 

10.8 

22 

121.7 

70.7 

I.O 

14.9 

83-7 

19-3 

4i-3 

14.9 

26.5 

23 

J33-4 

66.2 

i  .7 

14.7 

79.1 

21.5 

41.8 

14.7 

.... 

28.9 

24 

126.8 

69.7 

I.O 

14.8 

82.6 

19.7 

44-6 

14.8 



37.9 

25 

134-4 

67.4 

i-7 

14.7 

78.8 

21.  1 

45-9 

14.8 

29.0 

26 

83 

141 

132.6 

63.8 

24-7 

»s.« 

66.9 

19.6 

28.3 

6.7 

10.3 

35-o 

27 

62.7 

116.3 

112.3 

69.6 

26.0 

15-0 

70.2 

•5.. 

25-5 

5-o 

11.9 

32.1 

28 

65-7 

121.3 

122.3 

59.9 

25-3 

*.. 

63-6 

18.8 

28.3 

6.0 

"•3 

34-o 

29 

69 

114.2 

109.6 

69.6 

26.0 

14.8 

82.4 

15  7 

9-2 

3-3 

II.  0 

35-0 

30 

66 

no.  6 

107.2 

60.4 

25.8 

14.8 

73-2 

!6:7 

10.5 

4.1 

II.  0 

34-7 

31 

78.8 

130 

121.  1 

71.2 

25-8 

15.  i 

82.6 

14.0 

16.1 

4.2 

n.  6 

31-8 

32 

75 

132 

126 

67.0 

25  4 

15-1 

78.1 

i5-7 

16.9 

4-6 

ii.  i 

33-4 

33 

73-4 

128.4 

I23-7 

64.1 

25-3 

14.9 

76.1 

i5-4 

14-8 

4-3 

"•3 

32-4 

34* 
35 

75-5 
75-3 

119 
120.3 

"3-5 
117.1 

71.5 

68.2 

25.2 
25  -1 

14.6 
14-6 

ll'i 

12.5 
14.2 

10.6 
10.6 

4-5 
4-7 

10.3 
10.3 

25-8 
30.1 

36 

76.3 

in.  5 

109.  i 

68.5 

25-9 

14.8 

81.7 

15-3 

9-9 

3-9 

"•5 

34-o 

37* 

68.3 

112.  6 

107.6 

61.1 

25.8 

14.6 

74-o 

16.2 

10.5 

4-o 

10.9 

34-7 

38 

72.4 

120.5 

"9-5 

65.4 

25-3 

14.7 

77-8 

15-5 

12.3 

4  o 

"•3 

33-4 

39 

66 

114 

115-1 

71.6 

25-7 

14-8 

85.0 

12.  I 

9-9 

3-6 

28.0 

40* 

77-5 

122 

117.9 

71.8 

25-4 

14.8 

85-3 

I5-S 

10.5 

4.2 

ii  .  i 

33-6 

41* 

65-3 

III.3 

113-8 

69.9 

25.8 

14-8 

83.5 

16.6 

10.5 

4.0 

ii.  i 

36.5 

42* 

75-4 

II7.9 

120 

68.3 

24.9 

14.7 

81.7 

16.1 

12.3 

4-2 

"•3 

35-2 

43 

75-3 

120 

121.  6 

67.2 

25.0 

14.8 

80.7 

«t-J 

10.5 

4-4 

ii  .  i 

36.9 

2/8  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

TABLE  VIIL— Concluded. 


Revolutions. 

Horse- 

Water. 

Water  per  horse- 

power. 

power  per  hour. 

Total 
water 
from 
con- 
den- 
ser. 

Total 
water 
from 
jack's 
and 
steam 
chest. 

Propor- 
tion of 
water 
from 
jackets 
and 
steam 
chest. 

Water 
per 

hour. 

Propor- 
tion of 
total 
water 
shown 
by  indi- 
cator. 

Total 

Per 

hour. 

Per 
min- 
ute. 

Indi- 
cated. 

Net. 
** 

Per 

indi- 
cated 
horse- 
pow'r 
meas- 
ured. 

Per 
net 
horse- 
pow'r 
meas- 
ured. 

Per 

indi- 
cated 
horse- 
pow'r 
by  in- 
dica- 
tor. 

1 

4606 

2403 

40.1 

87.0 

73-2 

6722 

35i2 

0-635 

40.4 

47-9 

25-6 

2 

S5i7 

2452 

40.8 

90.2 

76.1 

8949 

3982 

0.673 

44  2 

52.3 

29.7 

3 

5i99 

2476 

41-3 

95-3 

81.1 

6716 

177 

0.026 

3J75 

0.779 

33.3 

39-2 

26.0 

4 

5434 

2547 

42.5 

97-9 

83-3 

7827 

165 

O.O2I 

3660 

0.871 

37.4 

43-9 

32.6 

5 

5468 

2467 

41.1 

89.7 

75-5 

6740 

292 

0.043 

3054 

0.789 

34.1 

40.4 

26.9 

6 

558o 

2536 

42.3 

102.9 

88.4 

7849 

243 

0.031 

3588 

0.830 

34.8 

40.6 

28.9 

7 

4558 

2580 

43 

122.8 

108.1 

5618 

3T95 

0.688 

26.0 

29.6 

17.9 

8 

5264 

2654 

44-2 

127.2 

112.  0 

6745 

.... 

3397 

0.692 

26  7 

3°-3 

18.5 

9 

6245 

3046 

50.8 

182.2 

164.8 

8980 

4373 

0.762 

24.0 

26.5 

18.3 

10 

6318 

3009 

50.1 

182.4 

l65.= 

10039 

.... 

4800 

0.725 

26.3 

29.1 

19.1 

11 
12 

7787 
7248 

3361 
3345 

56.0 
55-8 

236.9 
236.5 

217.7 
217-3 

13468 
J4474 

.... 

5800 
6645 

0-795 
0.790 

24  5 

28.1 

26.6 
30.6 

19.5 

22.2 

13* 

8113 

3161 

52.7 

219.5 

201.4 

16736 

.... 

6493 

0.882 

29.6 

32.2 

26.1 

14 
15 

5363 

5665 

2659 
2763 

44-3 
46.1 

121  .  I 
137.5 

105.9 
I2I.4 

5618 
673  T 

5^6 

428 

0.092 
0.066 

2778 
3295 

0.780 
0.717 

22.9 
24.0 

26.2 
27.1 

17.9 
17.2 

16 

6064 

2753 

45-9 

136.4 

120-7 

6736 

321 

0.048 

3°55 

0.777 

22  4 

25-3 

17.4 

17 

6691 

3018 

50.3 

163.3 

146.0 

8974 

416 

0.047 

4°55 

0.702 

24.8 

27.8 

17.4 

18 

6003 

2952 

49-2 

166.2 

M9-3 

7846 

332 

0.042 

3852 

0.742 

23.2 

25.8 

17.2 

19 

11509 

3069 

51-2 

185.2 

167.5 

17899 

553 

0.031 

4761 

0.721 

25.7     28.4 

I8.5 

20 

6816 

3272 

54-5 

213.0 

J94-3 

11229 

300 

0.027 

5388 

0-753 

25.31  27.7 

ig.O 

21 

8038 

3495 

58.2 

255-o 

235-0 

J56S4 

290 

O.Oig 

6763 

0.808 

26.5     28.8 

21-4 

22~ 

6164 

2801 

46.7 

169.6 

153-6 

11186 

6165 

0.796 

30.0     33-1 

23-9 

23 

6873 

3101 

Si-7 

204.8 

187.1 

13382 

.... 

6901 

o  837 

29.  4  i  32.1 

24.6 

24 

6085 

2968 

49-5 

189.6 

172.6 

10054 

"288 

O.O29 

6085 

0.940 

25.9 

28.4 

22.2 

25 

6761 

3194 

53-23 

212.2 

193-9 

12263 

429 

0.035 

6752 

0.864 

27.3 

29.9 

23.6 

26 

7128 

3719 

62.0 

297.8 

276.5 

14500 

7515 

0-757 

25.2 

27.2 

I9.I 

27 

7268 

3517 

58.6 

258.5 

238.4 

12334 

5i7 

0.042 

5946 

0.695 

23.0 

24.9 

16.0 

28 

7i3i 

3657 

60.9 

284.2 

263.2 

13422 

374 

O.O28 

6873 

0.783 

24.2 

26.1 

18.9 

29 

9°37 

3615 

60.2 

289.2 

268.5 

15707 

416 

O.O26 

6287 

0.750 

21.7 

23-4 

16.3 

30 

7402 

2611 

60.2 

286.8 

266.2 

13470 

234 

0.017 

6578 

0.758 

22  9 

24.7 

17.4 

31 

6548 

35o8 

58-5 

255-3 

235-2 

iin8 

459 

0.041 

5994 

0.660 

23.5 

25-5 

i5-5 

32 

7513 

3695 

61.6 

282.5 

261  .4 

14526 

301 

O.O2I 

7157 

0.654 

25.3 

27.4 

16.6 

33 

86941 

3630 

60.5 

268.6 

247.9 

I554I3 

6541 

0.696 

24.3 

26.4 

16.9 

34* 

6858 

3I4I 

52-4 

185.1 

167.1 

10088 

4633 

0.699 

25.0 

27.7 

J7-5 

35 

6890 

336i 

56.0 

231.4 

212.2 

11199 

.... 

55oi 

0.716 

23.8 

29.9 

17.0 

36 

7244 

3592 

59-9 

279.6 

259.0 

12343 

6120 

0.748 

21.9 

23-6 

16.4 

37* 

7075 

3567 

59-5 

282.9 

262.5 

13469 

6786 

0.707 

24.0 

25.8 

17.0 

38~ 

88552 

3692 

~o77 

281.6 

2OO-5 

148863 

5*57 

0.035 

6208 

0-757 

22.0 

23-8 

16.7 

39 

6798 

3067 

Si-i 

197.0 

179-5 

8962 

460 

0.051 

4036 

0.765 

20  5 

22.5 

!5-7 

40* 

7089 

3515 

58.6 

270.4 

250.3 

11196 

408 

0.036 

5573 

o.8n 

20.6 

22.3 

16.7 

41* 

7774 

3672 

61.2 

306.2 

285.3 

13450 

384 

O.O29 

6336 

0.797 

20.7 

22.2 

16.9 

42* 

16234 

3676 

6!.  3 

295.6 

274.6 

27978 

935 

0.033 

6331 

0.847 

21.4 

23.1 

18.1 

43 

7972 

4123 

68.7 

348.0 

324.4 

14542 

453 

0.032 

7475 

0.800 

21.5 

23-0 

17.3 

**  Estimated  friction  2.5  pounds  per  square  inch. 


TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES.          279 

•with  the  cylinder  thoroughly  steam-jacketed.     The  gain  from 
compounding  is 


when  the  consumptions  of  steam  are  compared  directly,  and  is 
21900—  19600 


when  the  thermal  units  per  horse-power  per  hour  are  com- 
pared. 

If  the  test  on  the  Rush  is  compared  with  the  test  on  the 
Reynolds-Corliss  engine  the  gain  is  a  little  less,  but  the  latter 
engine  has  the  advantage  of  much  higher  boiler-pressure. 

The  engine  of  the  Bache,  although  it  uses  steam  of  80  pounds 
boiler-pressure,  appears  to  require  nearly  ten  per  cent  more  steam 
per  horse-power  per  hour  than  the  Rush  does,  and  to  use  nearly 
as  much  steam  as  the  Reynolds-Corliss  engine  working  single 
and  without  a  steam-jacket.  In  this  comparison  it  is  to  be  borne 
in  mind  that  the  engine  of  the  Bache  was  a  tandem  compound 
engine,  having  a  steam-jacket  on  the  large  cylinder  only,  while 
the  engine  of  the  Rush  was  a  receiver  compound  engine,  with 
the  cranks  at  90°,  and  with  both  cylinders  thoroughly  jacketed. 
From  the  arrangement  of  the  cylinders  the  radiation  was  prob- 
ably much  less  than  the  radiation  from  the  engine  of  the  Bache. 
Also,  the  engine  of  the  Bache  was  considerably  smaller  than 
that  of  the  Rusli.  A  part  of  the  inferiority  of  the  engine  of 
the  Bache  should  be  attributed  to  the  forms  of  the  boilers. 
The  boiler  of  the  BacJie  was  designed  to  give  high  evaporation, 
consequently  the  steam  in  the  steam-chimney  did  not  receive 
much  heat  from  the  escaping  gases.  On  the  revenue  steamers 
the  boilers  were  designed  to  give  large  power  for  a  given  space, 
and  the  escaping  gases  in  the  steam-chimney  had  a  higher 
temperature,  and  consequently  the  steam  furnished  was  prob- 


28O  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

ably  drier.  It  appears,  therefore,  that  the  larger  cost  of  fuel 
per  pound  of  steam  made  when  the  proportion  of  heating 
surface  is  smaller,  may  be  compensated  in  part  by  a  smaller 
cost  of  power  in  pounds  of  steam,  on  account  of  superior  dry- 
ness. 

In  these  experiments,  however,  the  higher  evaporative 
efficiency  of  the  boilers  of  the  Bache  more  than  compensated 
for  the  greater  cost  of  power  in  pounds  of  steam,  as  the  follow- 
ing table  will  show : 


BACHE. 

RUSH. 

2O   <n2 

18  ^8d 

91^1 

7    ZtdQ 

2    227 

24-2C 

The  consumption  of  coal  in  case  of  the  Bache  was  calcu- 
lated from  the  performance  of  the  boiler  during  the  long  run 
(Table  VI,  Exp.  9),  assuming  the  efficiency  of  the  boiler  to  be 
the  same. 

The  gain  by  compounding  in  practice  is  frequently  claimed 
to  be  twenty  per  cent,  for  which  Mr.  Emery  gives  the  following 
explanation  :  In  high-pressure  condensing  engines  the  pressure 
is  seldom  maintained  at  the  point  designed.  This  occurs  from 
two  causes — the  carelessness  of  operating  the  engine,  or  the 
imperfect  adaptation  of  the  engine  to  the  purpose.  No  matter 
what  the  pressure  designed  may  be,  if  the  engine  is  designed 
to  work  with  considerable  expansion,  the  engineer  finds  that 
his  engine  works  more  smoothly,  and  with  less  trouble  to  him- 
self, with  less  pressure  and  less  expansion,  and  for  trivial  rea- 
sons lets  his  pressure  fall  or  partially  closes  the  throttle,  and 
lengthens  the  cut-off,  and  finally  believes  that  it  is  as  well  to 
work  in  that  way  all  the  time.  With  compound  engines  there 
are  fewer  difficulties  in  working  high-pressure  steam,  and  in 
most  cases  it  is  difficult  to  keep  up  the  speed  with  low  pres- 
sures. 

The  efficiency  of  the  boilers  of  the  several  steamers  was 


TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES. 


281 


tested  by  one  experiment  on  each,  of  sufficient  length  for  the 
purpose.     The  results  are  given  in  the  following  table : 
EFFICIENCY  OF  BOILERS. 


Coal  per  sq. 
foot  of  grate 
surface  per 
hour. 

Per  cent 
of  refuse. 

Water  evap- 
orated per 
pound  of  coal 
from  and  at 

212°. 

Coal  per 
horse-power 
per  hour. 

Bache  Table  VI  Exp  9 

8  84 

IQ  8 

Rush  Table  VI  f  Exp  i  

it  388 

8  5675 

Dexter,  Table  VII,  Exp.  5  
Dallas,  Table  VII,  Exp.  12  
Gallatin,  Table  VIII,  Exp.  38  

12.026 
13-313 
iS-305 

20.291 
20.503 
21.609 

8.6878 
8.7625 
7-4i8 

3-1313 
3.4267 
3.002 

If  we  compare  the  tests  stated  in  the  table  on  page  270,  it 
appears  that  the  use  of  a  steam-jacket  on  the  Bache,  when 
working  single,  was  accompanied  by  a  gain  of 


27600  —  24700 
27600 


=  o.io 


while  the  use  of  a  steam-jacket  on  the  Gallatin  was  accompa- 
nied by  a  gain  of 


23200  —  21900 
23200 


=  o.io  — -. 


In  Experiments  29  and  30  on  the  Gallatin  the  steam-jacket 
was  not  in  use,  but  the  condensed  water  was  drained  from  the 
valve-chest — probably  through  the  pipe  which  ordinarily  sup- 
plied the  jacket  when  it  was  in  use.  In  Experiments  31  and 
32  the  jacket  was  supplied  with  steam  directly  from  the  boiler, 
and  presumably  the  valve-chest  was  not  drained.  Comparing 
these  experiments  with  each  other  and  with  Experiment  41,  it 
appears  that  the  draining  of  the  steam-chest  was  of  more  im- 
portance than  the  use  of  a  steam-jacket.  In  some  engines  the 
whole  supply  of  steam  for  the  engine  is  passed  through  the 
steam-jacket  on  the  way  to  the  steam-chest ;  and  in  such  case 
the  steam  must  suffer  condensation  in  the  jacket,  and  enter 
the  cylinder  with  more  moisture  than  if  it  passed  directly  to 
the  steam-chest.  Such  engines  do  not  show  so  good  economy 
as  those  having  a  separate  supply  of  steam  to  the  steam-chest. 


282  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

The  gain  from  the  use  of  a  steam-jacket  on  the  large  cylin- 
der, only,  of  a  compound  engine  is  shown  by  comparing  the 
experiments  on  the  Bache  working  compound,  with  and  with- 
out the  jacket  in  use.  The  gain  is 

24500—  21700 


The  experiments  do  not  give  the  data  for  the  discussion  of 
the  saving  by  the  use  of  a  steam-jacket  on  a  compound  engine 
when  both  cylinders  are  steam-jacketed.  Should  we  compare 
the  test  on  the  Bache  without  the  jacket  in  use  with  the  test 
on  the  Rush  with  both  cylinders  jacketed,  it  would  appear  that 
there  is  a  great  gain  from  jacketing  both  cylinders,  and  that 
there  is  a  marked  gain  from  applying  a  steam-jacket  to  the 
small  cylinder  in  addition  to  that  on  the  large  cylinder,  but 
from  the  preceding  discussion  it  is  evident  that  such  a  com- 
parison would  be  illusive.  It  does  not  appear  probable  that 
the  jacketing  of  both  cylinders  of  a  compound  engine  would 
give  a  greater  gain  than  the  jacketing  the  cylinder  of  a  simple 
engine  ;  and  if  such  a  conclusion  is  admissible,  then  those 
experiments  appear  to  show  that  the  application  of  a  jacket  to 
the  large  cylinder  only  of  a  compound  engine  gives  as  great  a 
gain  as  the  gain  from  jacketing  the  cylinder  of  a  simple  engine, 
and  that  consequently  there  would  be  little  or  no  gain  from 
applying  a  jacket  to  the  small  cylinder  in  addition  to  one  on 
the  large  cylinder.  On  the  other  hand,  Rankine  *  states  that 
in  cases  where  a  steam-jacket  has  been  applied  to  the  small 
cylinder  only  the  heat  thus  applied  has  been  found  sufficient; 
but  Rankine  gives  this  statement  in  connection  with  a  wrong 
theory  of  the  action  of  a  steam-jacket,  i.e.,  that  it  prevents 
liquefaction  in  the  mass  of  the  steam  during  expansion,  and  he 
does  not  quote  experiments  to  substantiate  the  statement.  We 
must  consequently  await  further  experiments  on  this  point. 

It  may  be  of  interest  to  state  in  this  connection  that  a  steam- 
jacket  is  sometimes  applied  to  the  intermediate  cylinder  only 

*  Steam-engine,  page  396. 


TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES.         283 

of  a  triple-expansion  engine,  and  that  some  engineers  are  in 
the  habit  of  using  the  jacket  in  starting  the  engine,  but  not 
when  the  engine  is  working  under  normal  conditions. 

The  only  series  of  tests  that  can  be  used  to  determine  the 
number  of  expansions  to  be  used  with  a  compound  engine  are 
those  on  the  Bache,  which  show  that  the  best  economy  was 
attained  with  6  or  7  expansions  both  when  the  jacket  on  the 
large  cylinder  was  in  use,  and  when  it  was  not  in  use. 

To  show  the  gain  from  increased  steam-pressure,  the  follow- 
ing table  has  been  made.  The  greater  economy  of  the  engine 
of  the  Gallatin  as  compared  with  that  of  the  Dexter  may  be 
attributed  in  part  to  the  larger  size  of  the  former. 

STEAM-PRESSURE  AND  CUT-OFF,  SIMPLE  ENGINES. 


Boiler- 
pressure 
gauge. 

Cut-off 
fraction  of 
stroke. 

Steam  per 
horse- 
power per 
hour. 

Thermal 
units  per 
horse- 
power per 
hour. 

Relative 
economy 

21 

0.44 

S3-  T 

Mackinaw  

•34.0 

0.38 

Eutaw 

26    I 

Dexter  

68.7 

0.18 

Dallas                   

14    6 

^ 

it 

68  q 

.90 

23200 

Tests  on  the  Leila,  the  Siesta,  and  the  Gleam. — The 

engines  of  the  yachts  Leila  and  Siesta  were  built  by  the 
Herreshoff  Manufacturing  Co.,  and  were  tested  in  Narragansett 
Bay  by  Mr.  Isherwood  *  in  1880  and  1882.  The  engine  of  the 
yacht  Gleam  was  built  by  the  Fore  River  Engine  Co.,  of 
Weymouth,  Mass.,  and  was  tested  by  Messrs.  Roberts  f  and 
Sayer  of  the  Class  of  1888,  Massachusetts  Institute  of  Tech- 
nology. 

The  engines  of  the  Leila  and  Siesta  differed  only  in  size, 
those  of  the  latter  being  a  little  the  larger.  They  each  had 
two  cylinders, — one  high-pressure  and  one  low-pressure, — with 
the  cranks  at  right  angles.  Both  cylinders  of  each  engine  had 


*  Reports  to  the  Bureau  of  Steam  Engineering,  1881  and  1883. 
f  Thesis,  1888. 


284 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


a  plain  slide-valve  with  a  cut-off  valve  on  the  back  of  the  main 
valve,  the  main  valves  having  neither  lead  nor  compression. 
The  cylinders  were  lagged,  but  not  steam-jacketed.  The  boiler 
of  the  Leila  was  arranged  to  furnish  strongly-superheated  steam, 
but  that  of  the  Siesta  furnished  saturated  or  moist  steam. 

In  the  tests  on  the  Leila  the  condensed  steam  from  the  sur- 
face condenser  was  measured,  as  it  was  delivered  by  the  air- 
pump,  in  a  standard-gallon  measure.  The  condensed  steam 
from  the  surface  condenser  of  the  Siesta  was  measured  in  two 
measuring-tanks  of  known  capacity,  which  were  filled  and 
emptied  alternately. 

The  engine  of  the  Gleam  had  two  cylinders  with  the  cranks 
at  right  angles.  The  cylinders  were  lagged,  but  not  steam- 
jacketed.  Each  cylinder  had  a  piston  slide-valve  actuated  by 
a  Joy  valve-gear.  Steam  was  furnished  by  an  upright  tubular 
boiler  which  superheated  the  steam  enough  to  determine  its 
quality,  but  not  enough  to  affect  the  economy  of  the  steam 
consumption  to  any  marked  degree. 

The  dimensions  of  the  engines  of  these  three  yachts  are 
given  in  the  following  table : 

DIMENSIONS  OF  YACHT  ENGINES. 


Leila 

Siesta. 

Gleam. 

Number  of  cylinders                        

2 

io^ 

large  cylinder,      "        

16 

18 

piston-rod  small  cylinder,  inches  

i^ 

"          large         "            "      

& 

jKX 

Stroke,  both  pistons  

18 

18 

Displacement,  small  cylinder,  cubic  feet  

0.652 

0.891 

Head  -end.     Crank-end. 

large        "             "        "    
Clearance,  fraction  of  piston  displacement  — 
small  cylinder  

2.034 
0.088 

2.634 
0.094 

1.342        1.340 

o  068 

Ratio  of  volumes  of  cylinders             .         

2.962 

The  data  and  the  results  of  the  tests  on  the  yachts  Leila, 
Siesta,  and  Gleam  are  given  in  Tables  IX,  X,  and  XL 

Discussion  of  Results. — The  tests  on  the  engines  of  the 
Leila,  lettered  A  to  H,  were  made  with  substantially  the  same 
cut-off  and  the  same  number  of  total  expansions.  The  steam- 


TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES.         285 

pressure  was  diminished  progressively,  accompanied  by  a 
diminution  of  the  amount  of  superheating  and  of  the  speed  of 
revolution.  The  change  from  95  revolutions  per  minute  to 
220  revolutions  per  minute  is  not  enough  to  produce  a  marked 
change  of  economy ;  consequently,  the  regular  and  marked 
increase  of  steam  consumption,  or  of  the  consumption  of  ther- 
mal units,  per  horse-power  per  hour  is  due  to  the  decrease  of 
pressure  and  the  less  amount  of  superheating. 

The  remaining  experiments  were  made  to  determine  the 
effect  of  cutting-ofT  on  the  small  cylinder  only,  on  the  large 
cylinder  only,  and  of  not  cutting-off  on  either  cylinder.  Also 
the  gain  in  this  engine  from  compounding. 

Comparing  the  Experiments  C  and  I,  which  are  in  other 
respects  alike,  the  consumptions  of  thermal  units  per  horse- 
power per  hour,  with  and  without  a  cut-off  on  the  large  cylinder 
in  addition  to  the  cut-off  on  the  small  cylinder,  are  in  the  ratio  of 

19100  :  21000  ::  i  :  1.099. 

In  the  first  series  it  is  noticeable  that  the  distribution  of 
work  between  the  two  cylinders  of  the  engine  is  good,  and  is 
not  greatly  affected  by  the  change  of  pressure  and  of  super- 
heating. In  the  tests  I,  J,  and  K  an  excessive  amount  of 
work  is  done  in  the  small  cylinder.  On  the  other  hand,  the 
work  done  in  the  large  cylinder  is  excessive  in  the  tests  L  and 
M,  when  the  steam  is  cut  off  in  the  large  cylinder  only. 

The  total  number  of  expansions  is  not  affected  by  the  cut- 
off in  the  large  cylinder,  anct  is  nearly  the  same  for  experiments 
C  and  I.  The  gain  from  the  cut-off  on  the  large  cylinder  is  to 
be  attributed  to  the  diminution  of  the  drop  between  the  high- 
and  low-pressure  cylinders  and  to  the  better  division  of  the 
ranges  of  temperatures. 

When  the  steam  was  cut  off  in  the  large  cylinder  only  the 
total  number  of  expansions  depended  on  the  ratio  of  the  vol- 
umes of  the  cylinders  only,  and  was  much  less  than  when  the 
steam  was  cut  off  in  the  small  cylinder,  and  the  increased  con- 
sumption is  to  be  attrib;«:ed  mainly  to  this  cause. 


286 


THERMODYNAMICS  OF   THE  STEAM-ENGINE. 


TABLE 
TESTS  ON 


jj 

Cut-off  and 

Temperatures, 

Pressures,  pounds  on  the 

3 
C 

expansions. 

Fahrenheit. 

square  inch. 

a 

^ 

V 

V 

to 

o 

V 

1 

£  • 

V 

fe| 

S3 

in 

MANNER  OF 
RUNNING. 

ex 

i 

sL 

P 

£  *• 

jis 

6.2 

3  £ 

8 
a 

rt 
* 

rt 

w 

I 

•a 

^ 

kl 

?•" 

IH 

g^c 

3 
MI   qj 
If 

3^ 

te 

C  >» 

il 

if 

^  o 

c  g 

rt  <u" 

02    OJ 

3  B'~ 

r»S 

tl  JJ 

6  v 

_3 

•  o 

> 

2| 

o-^ 

J.  >. 

-iz 

o  v 

3.8 

^  a 

•S 

u 

.C 

S3 

"* 

fig 

«2i3 

VM    (A    K> 

II 

11 

S  S 

£° 

|§ 

^0 

f* 

u 

U 

H 

0 

o 

0 

o 

0 

ra 

w 

Steam  cut  off 

221. 
215- 

0.4 
0.4 

0.361 
0.336 

7.12 
7.12 

42 
45 

49 
49 

95-o 
93-S 

4J7 

355-2 
354  -o 

129.4 
127.2 

29.7 
29.0 

30.25 
30.25 

25.83 

26.07 

in  both 
cylinders  by 
independent 
cut-off 
valves. 

192. 

181. 
166. 
145. 
in. 

0.350 

0-335 
0-336 
0-353 
0.358 

0-335 
0.346 
0.371 
0.368 
0.376 

7.93 

8.21 
8.21 
7.89 
7.79 

55 
50 
54 
47 
47 

52 
47 
51 

52 
52 

76.3 
71.0 
68.0 
64.0 
60.0 

378 
366 
350 
320 
27Q 

340.6 
332.0 

302.3 
377-1 

104.5 
91.4 
75.0 
57  7 
32.4 

18.2    30.00 

15.9  29.98 
10.5    30.03 

5-5    SO-00 
—  o  8i  30.00 

25.92 

25-49 
26.32 
26.50 
26.50 

94. 

0.361    0.349 

7.74 

S2 

47 

64.0 

26l 

361  .0 

21.3 

—  2.4 

30.00 

25.18 

Steam  cut  off 
in  small  cylin- 
der only. 

188. 
167. 
145- 

0.329 
0.325 
o  347 

'.'.'.'. 

8.35 

8.42 
7.99 

43 
44 
44 

46 
47 
47 

76.0 
69-5 
64-5 

383 
356 

335 

340.2 
319-7 
3°3-4 

103.7 
74.6 

55.8 

—  O.I 

—  3-5 

—  5-2 

30.36 
30.36 
30.36 

24.41 

25.18 
25-58 

Steam  cut  off 
in  large  cylin- 
der only. 

197. 

122. 

.... 

0.297 
0.363 

3.20 
3.20 

38 
5° 

48 
47 

88.5 
64-5 

360 
304 

308.4 
260.5 

61.7 
21.0 

33-4 
8.0 

29.88 

30.06 

25-43 
25-93 

No  cut-off. 

189.5 

3.20 

43 

47 

91.0 

345 

304-6 

57.0 

4-9 

30-36 

25-05 

Small  cylin- 

der discon- 

nected; large 

191.5 

o-335 

2.66 

38 

47 

96.  s 

344 

292.3 

44.9 

40.7 

3°-I7 

25-59 

cylinder  used 

I47.6 



0.371 

2.43 

40 

47 

71.0 

304 

261.4 

21.4 

19.4 

30.  19 

25.98 

as  a  simple 

engine. 

In  Experiment  N  the  omission  of  the  cut-off  on  both  cylin- 
ders gave  a  fair  distribution  of  the  work,  but  the  drop  between 
the  cylinders  was  excessive,  and  the  consumption  was  larger, 
and  the  engine  was  consequently  less  economical  than  when 
the  large  cylinder  was  used  alone,  as  in  the  Experiment  O. 

The  gain  from  compounding  may  be  inferred  from  a  com- 
parison of  Experiments  G  and  H  with  Experiments  O  and  P  ; 
but  a  correct  conclusion  cannot  be  reached  from  these  experi- 
ments, nor  from  a  comparison  of  any  of  the  tests  in  the  table, 
since,  on  the  one  hand,  the  economy  of  the  large  cylinder  used 
as  a  simple  engine  would  be  improved  by  an  increase  of  pressure 
and  an  increase  of  the  total  number  of  expansions ;  and,  on  the 
other  hand,  the  steam-pressure  in  Experiments  G  and  H  is  too 
low  to  make  compounding  advantageous. 


TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES. 


287 


IX. 

LEILA. 


Pressures,  pounds  on  the  square  inch. 

Horse-power 
indicated. 

["'a. 

a 

Per  cent  of 
steam  in  the 

Small  cylinder,  absolute. 

Large  cylinder,  absolute. 

oc 

bis 

cylinder. 

Initial  pressure. 

Pressure  at  | 
cut-off. 

Pressure  at 
end  of  stroke. 

Mean  back 
pressure. 
Back  press're  at 
begin^g  of  st'ke 

Mean  effective 
pressure. 

V 

Pressure  at 
cut-off. 

Pressure  at  end 
of  stroke. 

*fi   <U 

c'^ 

Mean  back 
pressure. 

Mean  effective 
pressure. 

Small  cylinder. 

Large  cylinder. 

I  Aggregate. 

Steam  used  per 
power  per  ho 

Thermal  units  p 
horse-power  p 

Cut-off,  small 
cylinder. 

End  of  stroke, 
small  cylinder. 

IEnd  oi  stroke, 
large  cylinder 

134.8 
130.7 

118.9 
118.6 

60.8 

48-7 
46.7 

*4-7 

12.  S 

53-8 
S3-4 

45-5 
44.1 

2.0 

3-3 
2.7 

4-7 
4.8 

6.5 
6.1 

20.4 
20.3 

7.782.2 
65.679.6 

49-9 
45-2 

16.4 
16.0 

18400 
18100 

98 
90 

*I02 

*i°3 

81 
80 

109.0 
97.6 
83-7 
64.6 
42.5 
32.3 

100.4 
.92-5 

77.6 
58.8 
38-9 
30-5 

40.6 
38.8 
32.  3 
26.2 
18.8 
16.6 

33.229.7 
32.328.8 
25-322.4 
20.  o  17.0 
13.711.9 
12.6  ii.  6 

44-3 

39-5 

26.2 
I7.8 

12.8 

32.0 

III 

19.0 

12  .2 
II.  I 

6-3 
6.4 
8.9 

8.6 

9-7 
8.8 

5-o 
5-3 

4.1 
4.1 
3-3 
3-3 
3-3 
4.0 

4.8 
4-3 

I'l 

3-4 
4-3 

4-7 
3-7 

0-54 
8.05 
4.63 
3-4° 

48.451.5 
40.7  45.1 

21-721-3 
11.3    9-4 
6.9    5.9 

11 

63.6 
43-° 

20J 
12.8 

16.7 
17.4 

18.7 
20.9 
25.0 
32.7 

19100 
•20000 
21400 
23900 
28400 
37000 

i 

80 

67 

66 
56 

93 
93 

49 
78 

7b 
72 
74 
64 
45 
83 

114.2 

CO7-O 

43.0 

16.8 

is,  2 

63.6 

13.6 

10.9 

5-o 

S-S 

7-5° 

68.1 

2^.6 

9V 

18.5 

21000 

87 

96 

80 

87-3 

80.8 

3VS 

13-5 

12.6 

47-7 

IO-9 

Q.2 

4.4 

4-9 

4.8 

45-5JI4-8 

60. 

20.1 

23000   83 

96 

85 

.   66.7 

61.0 

26.5 

n.  6 

10.7 

36.6 

8-3 

.... 

7-5 

4-4 

4-7 

3-3 

30.4   8.8 

39- 

23.9 

27300 

75 

86 

80 

77-5 

66.4 

50.1 

44-5 

20.1 

48.2 

38.  s 

14.2 

^ 

•>••* 

23.6 

22.685. 

107. 

21.0 

23500 

*n 

8s 

[    33-1 

31.6 

22.5 

19.6 

18.1 

21.4 

iS-i 

7-2 

3- 

9.2 

12.6 

20. 

33- 

28.6 

32300 

83 

64 

70.6 

63.1 

22.6 

20.2 

43-9 

19-3 

... 

16.0 

4- 

6.0 

10.8 

47-3 

37- 

84. 

28.1 

31400 

. 

*IO 

86 

>   .... 

43-7 

17- 

4- 

6.1 

28.4 

Q8. 

08. 

25.5 

28200 

89 

> 

30-9 

24.9 

10. 

4- 

4.6 

i5-« 

42. 

42. 

32.0 

3570C 

81 

1 

*  Superheated. 

The  tests  on  the  Siesta  were  made  primarily  to  determine 
the  most  advantageous  cut-off  for  the  large  cylinder.  Now  the 
cut-off  of  the  large  cylinder  does  not  affect  the  total  number 
of  expansions,  nor  does  it  affect  the  aggregate  horse-power  of 
the  engine  seriously.  It  does  affect  the  pressure  in  the  inter- 
mediate receiver,  and  consequently  affects  the  division  of  power 
between  the  two  cylinders,  the  drop  between  the  cylinders,  and 
the  division  of  the  range  of  temperatures.  In  comparing  tests, 
those  should  be  chosen  in  which  all  essential  data  except  the 
cut-off  of  the  large  cylinder  are  substantially  the  same. 

The  indicator-diagrams  for  the  tests  B  and  C  are  shown  by 
Figs.  57  and  58.  In  the  first  the  cut-off  of  the  large  cylinder 
is  at  0.251  of  the  stroke,  and  the  steam  in  the  small  cylinder  is 


288 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


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TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES. 


289 


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290 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


expanded  down  to  the  back  pressure  in  that  cylinder.  The 
initial  pressure  in  the  large  cylinder  is  the  same  as  the  back 
pressure  in  the  small  cylinder  at  half-stroke,  and  is  greater  than 


EXPERIMENT  B. 

SMALL  CYLINDER. 

Scale.GO  Ibs.  — -1  inch. 


LARGE  CYLINDER. 

Scale,  30  Ibs.  —  1  inch. 


FIG.  57. 


LARGE  CYLINDER 

Scale,  30  Ibs.  .=  1  inch. 


FIG.  58. 


the  terminal  pressure  in  the  small  cylinder.  This  peculiarity  of 
the  back  pressure  in  the  small  cylinder  is  due  to  the  fact  that 
the  cranks  of  the  engine  are  at  right  angles.  In  the  test  C, 
which  has  the  cut-off  at  0.465  of  the  stroke,  there  is  a  drop  of 


TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES.         291 

about  4£  pounds  from  the  terminal  pressure  in  the  small  cylin- 
der to  the  initial  pressure  in  the  large  cylinder ;  owing  to  the 
rise  of  back  pressure  in  the  small  cylinder  at  half-stroke,  the 


EXPERIMENT  E. 

SMALL   CYLINDER 

Scale, 60  Ibs.  =  1  inch. 


FIG.  59. 


EXPERIMENT?.. 

SMALL   CYLINDER. 

Scale,80  Ibs.  —  1  inch. 


FIG.  60. 


drop  at  the  end  of  the  stroke  of  the  small  piston  is  greater  than 
this,  as  is  evident  from  the  diagrams,  Fig.  58.  The  ratio  of  the 
consumption  per  horse-power  per  hour  is 


21600  :  20500 
in  favor  of  Experiment  C. 


1.05 


292 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


A  similar  comparison  can  be  made  of  the  Experiments  E 
and  F.  In  Experiment  E  the  cut-off  is  at  0.237  of  the  stroke 
of  the  large  piston,  and  the  expansion  in  the  small  cylinder  is 
carried  down  to  the  back  pressure.  In  Experiment  F  the  cut- 
off is  at  0.452  of  the  stroke  of  the  large  piston,  and  there  is  a 
drop  of  about  4^  pounds  from  the  final  pressure  in  the  small 
cylinder  to  the  initial  pressure  in  the  large  cylinder,  but,  as 
with  Experiment  C,  the  drop  at  the  end  of  the  stroke  of  the 
small  piston  is  more  than  that.  The  ratio  of  the  consump- 
tions is 

21000  :  20500  ::  1.025  :  i 

in  favor  of  Experiment  F. 

These  two  comparisons  show  that  for  this  engine  under  the 
given  circumstances  the  cut-off  on  the  large  cylinder  should 
be  at  a  little  less  than  half-stroke  instead  of  at  about  quarter- 
stroke,  and  that  a  small  drop  at  the  end  of  the  stroke  of  the 
small  piston  is  permissible. 

The  diagrams  for  the  Experiment  H  are  shown  by  Fig.  6i» 
In  it  the  cut-off  of  the  large  cylinder  occurred  at  0.857  °f  tne 

EXPERIMENT  H. 

SMALL    CYLINDER, 

Scale,€0  Ibs.— J.  inch. 


LARGE  CYLINDER. 

Scale,40  Ibs.  -  1  inch. 


FIG.  61. 

stroke,  and  there  was  a  drop  of  about  15^  pounds  from  the 
final  pressure  in  the  small  cylinder  to  the  initial  pressure  in  the 
large  cylinder.  Compared  with  Experiment  F,  the  consump- 
tions are  in  the  ratio 

:  1.14  :  i 


23400  : 
in  favor  of  the  Experiment  F. 


TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES.         293 

The  conclusion  is  that  a  small  drop  is  allowable  or  even 
advantageous,  but  that  a  large  drop  is  deleterious. 

The  determination  of  the  most  advantageous  number  of 
total  expansions  is  made  difficult  by  the  varying  boiler-pressure. 
It  is,  however,  apparent  that  5.9  expansions  in  Experiment  D 
gave  a  better  economy  than  12.9  expansions  in  Experiment  A, 
although  the  steam-pressure  in  A  was  higher  than  in  D. 

Inspection  of  Table  X  shows  that  six  expansions  reduce 
the  pressure  at  the  end  of  the  stroke  in  the  large  cylinder  to 
about  ten  pounds  absolute.  It  is  probable  that  a  greater  num- 
ber of  expansions  would  not  give  greater  economy  for  this 
engine  with  the  given  steam-pressure,  though  this  fact  cannot 
be  conclusively  shown  from  the  tests  given. 

If  Experiment  D  on  the  Siesta,  with  5.9  expansions  and 
using  saturated  steam,  may  be  compared  with  Experiment  D  on 
iheLeita,  with  8.1  expansions  and  using  superheated  steam,  then 
it  appears  that  the  small  amount  of  superheating  in  the  latter 
had  less  effect  than  other  causes  that  are  commonly  considered 
to  be  of  secondary  importance,  since  the  test  on  the  Siesta 
shows  the  better  economy. 

The  tests  on  the  Gleam  were  made  with  the  boiler-pressure 
very  nearly  constant,  while  the  change  in  the  speed  of  revolu- 
tion was  too  small  to  produce  much  effect.  The  throttle-valve 
was  wide  open  during  all  of  the  tests,  and  the  power  of  the 
engine  was  varied  by  changing  the  cut-off  on  both  cylinders 
simultaneously.  The  tests  i  and  2,  3  and  4,  and  5  and  6,  were 
made  under  similar  conditions  for  each  pair.  The  last  test, 
number  7,  was  made  with  full  engine-power,  at  which  the 
boiler  was  unable  to  furnish  steam  without  undue  forcing.  The 
consumption  of  steam  for  the  five  last  experiments  is  nearly 
constant,  the  variation  in  consumption  under  like  conditions 
being  as  great  as  at  the  different  rates  of  expansion  from  4.39 
to  7.04.  The  consumption  for  10.81  appears  to  be  somewhat 
more  than  for  a  less  rate  of  expansion. 

Leavitt  Pumping-engine.* — Two  duty  tests  of  a  com- 

*  E.  D.  Leavitt,  Jr.,  Boston  Soc.  Civ.  Eng.,  1885. 


294  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

pound  pumping-engine  at  the  Boston  Main  Drainage  Works 
are  given  here  as  an  example  of  advanced  practice. 

The  engine  is  one  of  a  pair  of  two-cylinder  compound  beam- 
engines.  The  steam-cylinders  are  inverted,  and  act  on  oppo- 
site ends  of  a  short  beam  on  a  level  with  the  engine-room 
floor;  below  the  floor  are  two  single-acting  plunger-pumps, 
connected  one  to  each  end  of  the  beam,  directly  under  the 
steam-cylinders.  The  main  shaft  carrying  the  fly-wheel  is  mid- 
way between  the  lower  ends  of  the  steam-cylinders,  and  the 
crank  is  connected  to  one  end  of  the  beam  near  the  point  of 
attachment  of  the  links  from  the  steam-piston  and  the  pump. 
The  steam  from  each  end  of  the  high-pressure  cylinder  passes 
through  a  straight  passage  to  the  same  end  of  the  low-pressure 
cylinder,  and  in  these  passages  are  reheaters  made  of  brass 
tubes  supplied  with  boiler  steam,  through  which  the  exhaust 
steam  from  the  high-pressure  cylinders  passes,  and  by  which  it 
is  dried  or  slightly  superheated.  The  steam  for  the  high-pres- 
sure cylinders  is  not  superheated,  but  during  the  tests  was 
assumed  to  be  dry  and  saturated. 

The  diameter  of  the  high-pressure  cylinder  is  25-^  inches, 
and  that  of  the  low-pressure  cylinder  is  52  inches ;  the  stroke 
of  each  piston  and  of  the  pump-plungers  is  4  feet. 

Each  steam-cylinder  has  four  independent  valves,  operated 
by  cams  ;  the  cams  which  move  the  admission-valves  of  the 
high-pressure  cylinder  are  controlled  by  a  governor.  All  the 
other  valves  have  a  fixed  motion. 

The  following  description  of  the  tests  is  taken  from  Mr. 
Leavitt's  paper : 

The  engine  tested  is  known  as  Engine  No.  3,  and  was  sup- 
plied with  steam  from  Boiler  No.  2. 

The  intended  duration  of  each  test  was  twenty-four  hours. 

The  method  of  making  the  tests  was  as  follows :  Steam  was 
raised  in  the  boiler  until  the  pressure  was  sufficient  to  run  the 
engine.  The  fires  were  then  drawn,  the  ash-pits  carefully 
cleaned,  and  new  fires  were  started.  It  was  desired  to  deter- 
mine the  quantity  of  water  pumped,  by  actual  measurement, 
in  the  reservoir  at  Moon  Island,  and  since  stopping  the  engine 


TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES.         2$$ 

would  have  caused  large  fluctuations  of  level  in  the  connecting 
sewers,  and  so  prevented  accuracy  of  measurement,  it  was  de- 
cided to  keep  the  engine  running  at  a  constant  rate.  This  was 
done  by  furnishing  the  engine  with  steam  from  Boiler  No.  3 
until  a  few  minutes  after  the  new  fires  were  started,  when,  by 
operating  the  valves  rapidly  and  simultaneously,  Boiler  No.  3 
was  shut  off,  and  the  engine  took  steam  from  No.  2,  thus  be- 
ginning the  engine  test.  The  engine  counter  was  read  at  the 
instant  the  test  began,  and  the  other  necessary  observations 
were  taken.  The  steam-pressure  was  increased  from  about  70 
pounds  at  the  start,  until  it  reached  100  pounds,  at  which  it 
was  kept  constant  until  near  the  end  of  trial,  when  the  fires 
were  burned  as  low  as  possible,  the  steam  pressure  dropping 
in  consequence.  When  the  pressure  and  height  of  water  in 
the  boiler  were  the  same  as  at  the  beginning  of  the  experiment, 
the  final  observations  were  taken,  and  the  fires  were  drawn. 
The  refuse  was  then  spread  upon  the  floor  to  cool.  The  un- 
burnt  coal  was  picked  from  the  ashes  and  weighed.  This 
weight  (averaging  less  than  one  per  cent  of  the  total  coal)  was 
deducted  from  the  gross  amount  of  coal  charged.  The  valve 
between  Boiler  No.  2  and  Boiler  No.  3  is  supposed  to  have 
been  tight,  but  to  avoid  increasing  the  duty  by  any  leakage,  the 
pressure  in  the  latter  was  kept  lower  than  in  the  former. 

The  height  of  the  sewage  in  the  pump-well  was  determined 
by  a  float-gauge,  tested  before  each  trial ;  the  load  on  £he 
pump  by  a  mercurial  gauge,  attached  to  the  force-main  of  an- 
other engine.  This  gauge  represented  the  height  in  the  pipe- 
chamber  at  the  end  of  the  force-mains,  and,  to  get  the  actual 
pressure  pumped  against,  it  was  necessary  to  add  the  friction 
in  the  force-main  used.  During  the  second  test  the  actual 
pressure  against  which  the  pumps  were  working  was  measured 
by  the  elevation  of  the  surface  of  water  in  a  box  at  the  top  of  a 
pipe  connected  with  the  force-main  a  few  feet  from  the  pump. 
A  comparison  of  this  gauge  with  the  mercurial  one  gave  a  cor- 
rection for  friction  in  the  force-main  to  use  with  the  first  test. 

Dry  Cumberland  coal  from  the  Pocahontas  Mine  was  used 
during  the  trial.  It  was  fed  to  the  boiler  from  a  car  holding 


296  THERMODYNAMICS  OF   THE  STEAM-ENGINE. 

about  1200  pounds.  During  the  first  test  the  car  and  contents 
were  reweighed  at  the  end  of  each  half-hour,  and  during  the 
second  test  after  each  firing. 

The  steam-pressures  at  the  boiler  and  the  pressures  and 
vacuum  at  the  engine  were  determined  by  Bourdon  gauges, 
which  had  been  previously  tested. 

The  temperature  of  the  steam  was  taken  by  a  thermometer 
inserted  in  the  main  steam-pipe  within  a  few  feet  of  the  boiler. 
This  thermometer  was  broken,  so  that  readings  could  not  be 
taken  during  the  second  test. 

The  barometer  was  an  aneroid,  placed  in  the  engine-room. 

The  quantity  of  water  fed  to  the  boiler  was  measured  in 
the  following  manner:  A  barrel,  holding  about  150  gallons,  was 
placed  upon  a  tested  platform-scale,  and  supplied  with  cold 
water  from  the  Cochituate  main,  and  also  with  condensed 
water  from  the  reheaters  and  steam-cylinder  jackets.  During 
the  second  test  the  exhaust  steam  from  the  boiler  feed-pump 
was  condensed  in  a  small  barrel  placed  above  the  weighing 
barrel,  into  which  it  was  drawn  from  time  to  time. 

After  having  been  weighed  the  water  was  run  into  a  large 
tub,  from  which  the  feed-pump  drew  its  supply.  The  meas- 
urement of  the  feed-water  was  checked  by  a  Worthington 
water-meter  placed  between  the  feed-pump  and  the  feed-water 
heater. 

To  ascertain  approximately  the  amount  of  water  returned 
from  the  cylinder-jackets  and  reheaters  the  amount  of  cold 
water  used  was  measured  during  the  second  test  by  a  meter 
placed  on  the  Cochituate  supply. 

About  seven  hours  after  the  beginning  of  the  first  test  a 
small  leak  was  discovered  from  a  safety-valve  on  the  boiler 
feed-pipe  between  the  pump  and  the  hot-water  meter.  After 
being  discovered,  the  water  leaking  was  caught  and  returned 
to  the  feed-pump  tub.  For  a  period  of  about  fourteen  hours 
the  leakage  was  weighed,  and  the  rate  so  determined  was  used 
to  make  a  correction  for  the  time  before  the  leak  was  discov- 
ered. The  total  amount  of  this  correction  was  650  pounds. 

On  the  second  test  all  pipe  connections  with  feed-pipes, 


TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES. 


297 


boilers,  and  engine,  except  those  in  use,  were  disconnected  to 
avoid  all  chance  of  error  from  leakage. 

Temperatures  of  the  feed-water  were  taken  before  and  after 
passing  through  the  feed-water  heater  by  means  of  thermome- 
ters inserted  in  the  feed-pipe. 

A  thermometer  in  a  tube  partially  filled  with  oil  was  in- 
serted in  the  flue  to  ascertain  the  temperature  of  the  gases 
beyond  the  feed-water  heater,  and  on  the  second  test  a  similar 
thermometer  was  placed  in  the  flue  between  the  boiler  and 
heater. 

Throughout  the  trials  half-hourly  observations  were  made 
of  the  engine-counter,  pressure  of  steam  at  engine  and  boilers, 
vacuum  in  condenser  in  inches  of  mercury,  height  of  water  in 
boiler,  height  of  water  in  tub  holding  feed-pump  supply,  water- 
meters  on  boiler  feed-pipe  and  cold-water  pipe,  barometer, 
temperature  of  steam,  temperature  of  gases  in  flue,  and  tem- 
perature of  engine-room.  Fifteen-minute  readings  were  taken 
of  the  force-main  and  pump-well  gauges,  and  readings  of  the 
feed-water  thermometers  every  ten  minutes. 

Temperatures  of  the  external  air  and  indicator-diagrams 
from  the  steam-cylinders  were  taken  hourly. 

A  large  number  of  observers  were  employed,  and  care  was 
taken  to  secure  accuracy  in  all  of  the  observations.  The  more 
important  records  were  taken  independently  by  assistants. 

No  calorimeter  tests  were  made  to  ascertain  the  quality  of 
the  steam.  For  the  purposes  of  calculation  it  has  been  as- 
sumed that  all  of  the  water  was  evaporated  into  dry  steam. 

RECORD  OF  TWO  DUTY  TESTS  OF  ENGINE  No.  3  (LEAVITT),  AT  THE 
BOSTON  MAIN  DRAINAGE  WORKS. 


First  Test. 

Second  Test. 

T. 

Date  of  trials  

Mar.  24—25  '85. 

May  i—2    1885 

2. 

Time  of  beginning  trial     .              . 

IO  06  A  M 

IO   31    AM 

3. 

Duration  

4. 

IQ  ^26 

IQ  ^72 

5. 

Revolutions  per  minute 

13    17 

I  -I    A  2 

6. 
7- 

Displacement  of  pumps  per  revolution   .  .  . 
Distance  from  o  of  gauge  down  to  sewage 
in  pump-well  

226.19  cu'  ft- 

ii  68  ft 

226.  19  cu.  ft. 

15    48    ft 

298 


THERMODYNAMICS  OF  THE   STEAM-EKGINE. 


First  Test. 

Second  Tesl. 

8.     Height   of    sewage     in    pipe-chamber,   as 
given  by  mercurial  gauge,  graduated  to 
give  equivalent  height  of  column  of  fresh 
water  

2e   76  ft 

26   <^H  ft 

9.     Pressure  in  force-main,  near  the  pump,  as 
indicated   by  column  of   frfesh  water  at 
temperature  55°  F   

26.0=5  ft 

IO.     Correction  of  mercurial  gauge  for  friction 
in    force-main,  from  data   furnished  by 
comparison  of  No.  8  and  No.  9  

o  36  ft 

II.     Total  lift  

37   80  ft 

4.2   43   ft 

12.     Weight  of  fresh  water  per  cubic  foot 

62  42  Ibs 

62  40  Ibs 

13.     Total  weight  of  dry  coal  consumed   

8  307  Ibs 

9  478  Ibs 

14.     Duty  of  engine  as  developed  by  the  trials: 
i-t  trial  I9526  X  226'19  X  37'8°  X  62'42  _ 

83.07 
~A  .^1  J9372  X  226.19  X  42.43  X  62.40 

125,450,000* 

122  dOO  OOO 

94.78 
15      Mean  pressure  of  steam  in  boilers           .  .  . 

QQ.  4.  Ibs 

98.6  Ibs 

16.     Mean   pressure  of  steam  in   main  steam- 
pipe  near  engine                                      .  . 

96  i  Ibs 

17      Mean  vacuum  in  condenser               .    . 

28.  i  in 

28  o  in. 

18.          "     atmospheric  pressure  by  barometer. 
19.          "     temperature  of  air  in  engine-room.  . 
20           "               "           of  external  air  

30.18  in. 
67.5  deg. 
oi  7  deer 

29.81  in. 
75.2  deg. 
40.6  dee. 

21.     Total  volume  of  sewage  pumped  by  plun- 
ger displacement 

33  038  ooo  gfals 

32  778  ooo  gals. 

22.     Total  volume  of  sewage  pumped,  as  actu 

30,224,000  gals. 

31,  256,000  gals. 

23      Average  slip  of  pumps 

8  .  5  per  cent.'f 

4.6  per  cent 

24.     Indicated  horse-power,  as   determined   by 
the  measurement  of  two  sets  of  cards  for 

251.5  H.  P. 

290.2  H.  P. 

25.     Horse-power  in  sewage  lifted,  pump  meas- 

212.9  H.  P- 

243.  5  H.  P. 

26.     Work  done  by  pump  in  per  cent,  of  indi- 
cated horse-power             

84.66  per  cent. 

83.90  per  cent. 

27.     Coal  burned  per  hour  per  indicated  horse- 
power                                                      .  .  . 

i  .  33  Ibs. 

1.35  Ibs. 

28.     Steam  per  indicated  horse-power  per  hour. 

13-9 

14.2 

*  To  reduce  this  duty  on  the  first  trial  to  the  usual  standard,  it  is  necessary  to  make  a  cor- 
rection for  the  coal  used  to  supply  steam  to  the  feed-pumps.  Assuming  the  duty  of  the  feed- 
pump to  be  10,000,000,  the  corrected  duty  of  the  pumping-engine  is  122.500,000. 

t  At  the  end  of  the  first  test  it  was  found  that  two  of  the  rubber  discharge-valves  had  been 
torn  off,  which  accounts  for  the  large  slip.  A  study  of  the  question  indicated  that  this  would 
not  materially  affect  the  duty,  a  view  which  is  corroborated  by  the  uniform  relation  between 
the  indicated  and  the  actual  horse-power  in  the  two  tests.  The  loss  of  action  in  the  pumps, 
when  the  valves  were  less  worn,  was  about  2.5  per  cent. 


TESTS  OF  SIMPLE  AND   COMPOUND  ENGINES. 


299 


RECORD  OF  TWO  TESTS  OF  BOILER  No.  2,  AT  THE  BOSTON  MAIN  DRAINAGE 
WORKS,  MADE  IN  CONNECTION  WITH  ENGINE  TESTS. 


First  Test. 

Second  Test. 

I       Date  of  trial                  ....     .  *    ........... 

Mar    24—25    '85 

May  1—2    1885 

o  58  A  M 

IO    2^    A  M 

24h    5im 

2j.h    oim 

DIMENSIONS  AND  PROPORTIONS. 
The  general  description  of  the  boiler  is 
given  in  Mr.  Leavitt's  paper. 
3      Grate  surface     

41:   c  gq    ft 

AC.   e  so   ft 

5.50  "     " 

5,Q                 «                   H 

4      \Vater-heatin0"  surface                      . 

I  826     "     " 

I         826                         "                    " 

5      Super-heating  surface     . 

6    "     " 

6      "     " 

5<z    Heatin0"  surface  in  feed-  water  heater  

Q34     "      " 

Q^4        "       " 

6.     Ratio    of    water-heating   surface    to   grate 
surface      .  .                . 

4O—  I 

ACt—  T 

AVERAGE  PRESSURES. 
7      Steam-pressure  in  boiler  by  gauge     .  .      . 

QQ   4  Ibs 

4U—  1 

98  6  Ibs 

8      Absolute  steam-pressure  

114.  2   " 

TT-J      2       " 

9.     Atmospheric  pressure  by  barometer  

30.  18  in 

29  81  in 

AVERAGE  TEMPERATURES. 

qi.  7  deer 

j.o  6  dec1 

jo      Of  steam           »  .        

O  -1Q     Q     *  * 

14.     Of   escaping   gases    before    passing   feed- 

I4<7.   Of  escaping  gases  after  passing  feed-water 
header     . 

rga    e  deP" 

4oy  ucs- 

15      Of  feed-water  before  passing  heater       .  .  . 

06  ^  des" 

I5<z    Of  feed-water  after  passing  heater  

IAC    i  (Jeff 

<?8  dee- 

FUEL. 
18.     Dry  coal  consumed  

8  307  Ibs 

T-      i      c       j      \  ist  test,  432  Ibs..  . 

5.2  per  cent 

19.     Total  refuse  dry  J2d     „  '  ^    „  

5  2  per  cent 

20.     Total  combustible  (weight  of  coal,  item  18, 

7  87^  Ibs 

8  981  Ibs 

0-74.    a  Ibs 

<7Q2    a  Ibs 

^16.0  Ibs 

371  8  Ibs 

WATER. 
26.     Total  weight  of  water  pumped  into  boiler 
and  apparently  evaporated  

86  783  Ibs 

98  780  Ibs 

260;.  Check  on    above    measurement   by  meter 
measurement    

85  620  Ibs 

06  622  Ibs 

26^.    Per  cent  less  by  meter  

i  3  per  cent 

26^.    Feed  water  taken   from  Cochituate  main, 
meter  measurement  

78  816  Ibs 

THERMODYNAMICS  OF  THE   STEAM-ENGINE. 


First  Test. 


Second  Test. 


28. 


29. 


30. 


32. 


33- 


34- 


ECONOMIC  EVAPORATION. 
Water  actually   evaporated  per  pound   of 
dry  coal,  from  actual  pressure  and  tem- 
perature   

Equivalent  water  evaporated  per  pound  of 
dry  coal  from  and  at  212°  F. : 

Including  f.w.h 

Excluding  f.w.h 

Equivalent  water  evaporated  per  pound  of 
combustible  from  and  at  212°  F.: 

Including  f.w.h 

Excluding  f.w.h 

COMMERCIAL  EVAPORATION. 

Equivalent  water  evaporated  per  pound  of 

dry  coal,  with  one  sixth  refuse,  at  70  Ibs. 

gauge-pressure,    from    temperature    of 

100°  F.  =  item  33  multiplied  by  0.7249: 

Including  f.w.h 

Excluding  f.w.h 

RATE  OF  COMBUSTION. 
Dry  coal  actually  burned  per  square  foot 
of  grate  surface  per  hour 


RATE  OF  EVAPORATION. 
Water   evaporated   from  and   at  212°  F. ; 
per  sq.  ft.  of  heating  surface  per  hour, 
excluding  f.w.h 


COMMERCIAL  HORSE-POWER. 
On  the  basis  of  30  Ibs.  of  water  per  hour 
evaporated  from  temperature  of  100°  F. 
into   steam   of   70  Ibs.   gauge-pressure 
(  =  34s  Ibs.  from  and  at  212°): 

Including  f.w.h 

Excluding  f.w.h 


10.45 


12.12  Ibs. 
1 1. 60  Ibs. 


12.78  Ibs. 
12.23  Ibs. 


9.26  Ibs 
8.87  Ibs 


7-35 


2.12  Ibs. 


117  H.  P. 
112  H.  P. 


10.42  Ibs. 


11.83  Ibs. 
11.35  Ibs. 


12.48  Ibs. 
11.98  Ibs. 


9.05  Ibs. 
8.68  Ibs. 


8.62  Ibs. 


2.44  Ibs. 


134  H.  P. 
129  H.  P. 


CHAPTER   XVII. 

HIRN'S     ANALYSIS. 

THE  best  insight  into  the  actual  behavior  of  steam  in  the 
cylinder  of  an  engine  is  given  by  Hirn's  analysis,  and  tests  giv- 
ing sufficient  data  for  such  an  analysis  are  of  special  interest 
and  importance,  since  they  indicate  why  one  method  of  run- 
ning an  engine  gives  a  better  result  than  another. 

Hirn*  gives  the  data  and  the  analysis  of  four  such  tests, 
made  on  engines  with  and  without  a  steam-jacket,  and  using 
moist  or  superheated  steam,  which  will  not  be  quoted  here, 
since  the  same  ground  is  covered  by  later  experiments  made 
under  his  direction  or  inspiration. 

The  most  notable  tests,  recorded  in  Tables  XII  to  XV,  are 
given  by  Hallauer.f  Many  of  the  tests  were  made  by  him 
personally,  and  all  were  worked  up  by  him  from  the  original 
data. 

Hallauer's  Tests  on  Simple  Engines.— In  Table  XII  are 
given  the  data  of  tests  made  on  an  engine  designed  by  Hirn 
to  use  superheated  steam.  It  had  four  independent  flat  valves 
moved  by  cams.  These  are  all  the  tests  given  by  Hallauer  in 
which  the  complete  data  are  given ;  in  all  other  tests  some  of 
the  data  are  missing,  and  the  results  and  conclusions,  only,  are 
given  here. 

In  Table  XII  are  given  the  results  of  these  tests  and  of  tests 
made  on  an  engine  of  the  Corliss  type  with  a  steam-jacket. 

Though  it  is  not  so  stated  in  Hallauer's  memoires,  it  ap- 
pears that  during  these  tests  these  engines  were  coupled  with 
another  engine,  and  that  the  speed  was  controlled  by  that  en- 
gine, with  the  intention  that  the  point  of  cut-off  and  the  work 
of  the  engine  should  remain  constant  during  a  test.  The  same 

*  Theorie  mecanique  de  la  chaleur.     1876. 

f  Bulletin  de  la  Soc.  ind.  de  Mulhouse,  vols.  xlvii.-liii.  ;  1877-1883. 

301 


302  THERMODYNAMICS  OF   THE  STEAM-ENGINE. 

method  seems  to  have  been  employed  during  most  of  the  tests 
of  compound  engines  given  in  Table  XIV. 

Observations  Taken. — (i)  The  steam  consumed  was  deter- 
mined by  measuring  the  feed-water  in  a  tank  alternately  filled 
and  emptied.  The  level  of  the  water  in  the  boiler  was  noted^ 
evening  and  morning,  and  allowance  made  for  the  difference ; 
also,  the  absence  of  leaks  was  made  certain  by  applying  hydrau- 
lic pressure  to  the  boiler,  pipes,  and  so  forth. 

(2)  The  water  rejected  by  the  air-pump  was  gauged  by  al- 
lowing it  to  flow  through  an  orifice  in  a  copper  plate  under 
considerable  head.     The  flow  through  the  orifice  used  was  de- 
termined by  direct  experiment  under  the  conditions  which  ob- 
tained during  the  experiment. 

(3)  The  superheating,  when  it  occurred,  was  measured  di- 
rectly by  a  good  mercurial  thermometer  placed  in  a  tube  let 
into  the  steam-pipe  near  the  engine-cylinder. 

(4)  The  per  cent  of  water  mixed  with  the  steam,  when  satu- 
rated steam  was  used,  was  determined  by  calorimetric  experi- 
ments.    In  some  cases  this  quantity  appears  to  have  been  in- 
ferred from  experiments  made  at  other  times  under  similar 
conditions. 

(5)  The  rise  of  temperature  of  the  injection-water  in  Hal- 
lauer's  own  work  was  determined  by  a  differential   air   ther- 
mometer reading  to  one  fiftieth  of  a1  degree  Centigrade. 

(6)  Other   temperatures  were    taken  with   mercurial   ther- 
mometers, or  were  deduced  from  the  indicated  pressures,  by 
aid  of  tables  of  the  properties  of  steam. 

(7)  The  work  was  measured  by  aid  of  a  good  steam-engine 
indicator,  and  in  some  cases  by  Hirn's  flexion  pandynamome- 
ter,  which  utilized  the  beam  of  the  engine  as  a  spring  for  meas- 
uring the  force  exerted  by  the  steam  on  the  piston.     As  before 
indicated,  the  diagrams  thus  obtained  also  gave  the  pressures 
at  the  several  interesting  points  of  the  stroke,  from  which  the 
temperatures  were  determined. 

(8)  The  revolutions  per  minute,  steam-pressure,  and  other 
required  observations,  were  taken  by  aid  of  proper  instruments. 


HIKN'S  ANALYSIS.  303 

The  greater  part  of  Tables  XII  and  XIII  is  sufficiently  in- 
telligible from  the  preceding  account  of  the  observations 
taken,  and  from  the  headings  of  the  columns.  The  following 
explanation  will  make  the  rest  clear : 

The  real  cut-off  given  in  column  5  of  both  tables  is  the 
ratio  of  the  volume  of  steam  in  the  cylinder  at  cut-off  to  the 
volume  at  the  end  of  the  stroke ;  it  is  therefore  the  reciprocal 
of  the  number  of  expansions. 

In  Table  I,  the  absolute  pressures,  in  columns  11-18,  were 
measured  on  the  indicator-cards,  and  the  temperatures  corre- 
sponding were  taken  from  tables  of  the  properties  of  steam. 

The  works  in  the  same  table  were  obtained  by  measuring 
the  appropriate  areas  on  the  indicator-card  with  the  polar 
planimeter.  The  corresponding  quantities  of  heat  were  ob- 
tained by  dividing  by  424. 

In  Table  XIII,  column  9,  the  net  horse-power  for  experi- 
ments 9-1 1  is  deduced  by  comparison  with  other  experiments, 
for  which  the  power  was  measured  by  a  brake. 

In  the  same  table,  column  10  shows  that  the  work  required 
to  expel  the  steam  from  the  cylinder  varies  widely,  as  com- 
pared with  the  total  absolute  work  during  the  forward  stroke. 
This  is  due  in  part  to  the  varying  power  of  the  forward  stroke, 
and  in  part  to  the  variation  in  the  vacuum  maintained  in  the 
condenser.  To  make  proper  comparisons  of  different  engines, 
the  back  pressure  should  be  the  same  in  all,  or,  as  that  is  sel- 
dom possible,  they  should  be  reduced  to  a  common  back  pres- 
sure. The  simplest  and  the  customary  reduction  is  to  assume 
that  the  back  pressure  is  zero,  or  that  the  vacuum  is  perfect. 

The  assumption  just  made  gives  rise  to  a  term  called  total 
or  absolute  horse-power,  i.e.,  the  horse-power  the  engine  would 
have  if  it  exhausted  into  a  perfect  vacuum,  and  usually,  if 
there  were  no  compression. 

The  consumption  of  dry  saturated  steam,  columns  11-13,  is 
deduced  from  the  actual  consumption  of  superheated  or  moist 
steam,  by  multiplying  by  the  heat  required  to  raise  one  pound 
of  water  from  freezing-point  to  the  pressure  and  condition 


304  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

stated,  and  then  dividing  by  the  total  heat  of  saturated  steam 
at  the  same  pressure.  In  two  cases  the  steam  for  total  horse- 
power  is  the  actual  weight  of  superheated  steam,  and  for  the 
same  experiments  the  consumption  per  net  horse-power  is  not 
given.  Again,  the  net  horse-power  is  not  stated  for  any  of  the 
experiments  on  the  Hirn  engine.  These  several  inconsisten- 
cies, and  others,  found  in  these  tables  and  in  Tables  XIV  and 
XV,  are  due  to  the  fact  that  they  are  condensed  from  calcula- 
tions and  tables  given  by  Hallauer  in  several  different  me- 
moires,  which,  being  for  specific  purposes,  included  such  of  the 
experiments  as  were  convenient.  As  the  details  of  some  of 
the  calculations  are  not  explicitly  stated,  I  have  not  thought 
it  profitable  to  supply  the  omissions. 

In  the  work  of  Hirn  and  Hallauer,  the  heat  QCJ  rejected 
from  the  walls  of  the  cylinder  during  exhaust  to  the  condenser, 
receives  special  attention,  and  is  the  only  one  of  the  several 
quantities  Qay  Qb,  Qcy  and  Qd,  which  is  directly  calculated  by 
them.  Hallauer's  calculations  are,  however,  in  such  form  that 
the  other  quantities  may  be  easily  deduced  from  them  with 
good  degree  of  approximation.  In  Table  II  I  have  stated  the 
quantities  Qa  and  Qb  thus  obtained  ;  Qd  is  not  regarded,  as  the 
compression  was  very  slight.  For  the  same  reason,  and  be- 
cause the  engines  usually  had  a  good  vacuum  in  the  condenser, 
the  weight  M0  is  neglected. 

In  Experiment  8,  when  the  condenser  was  not  used,  and 
where  the  steam  was  strongly  superheated  and  much  wire- 
drawn by  throttling,  "the  heat  rejected  to  the  condenser  be- 
comes —  1.2  per  cent,  a  result  which  is  impossible.  In  this 
test  {he  condenser  was  not  used,  and  no  check  on  this  quan- 
tity could  be  made.  This  discrepancy  may  be  due  to  the 
fact  that  the  steam  was  superheated  throughout  its  passage 
through  the  engine  ;  or  it  may  be  the  error  of  the  test. 

Hallauer's  Method  of  Calculation. — To  show  this  method 
and  compare  it  with  the  theory  developed  on  page  185,  an 
example  will  be  given,  using  the  test  on  the  Hirn  engine  made 
Sept.  7,  1875.  This  test,  with  some  others  on  the  same  en- 


HIRN'S  ANALYSIS. 


305 


TABLE  XII. 
DATA  OF  TESTS  ON  HIRN  ENGINE. 


I 

c 

O  rt 

Jl 

ii 

Hi 

y 

Date. 

Condition. 

Is 

9« 

vK 

•S3-2, 

"o-o  (j- 

3  3 
O.S 

0  o 

•&§! 

•ail 

lc-§8 

|S 

£*3 

£a" 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

1 

Nov.   18,  1873 

Superheated,  230° 

30.1736 

0.2570 

0.3065 

9-35oo 



2 

3 
4 

Nov.   28,  1873 
Aug.    26,  1875 
Aug.    27,  1875 

Saturated, 
Superheated,  215° 
Superheated,  223° 

30-5494 
29.969 
30.306 

0.2570 
0.2139 
0-4539 

0.3732 
0.2651 
0.2822 

9.29175 
8.7291 
8-5983 

0.0037 

5 

6 

Sept.     7,  1875 
Sept.     8,  1875 

Superheated,  195° 
Saturated, 

29  98 
30.41 

0.1628 
0.1628 

0.2240 
0.2634 

8-7384 
8.9132 

0.0030 

7 

Sept.    29,  1875 

Superheated,  220° 

30.13 

0-4539 

0.2265 

5-9810 



8 

Oct.     28,  1875 

Superheated,  220° 

30.00 

0.2867 

0.2714 

Temperatures  of 

Absolute  pressures  in  kilos  per  sq.  m.,  and  corresponding  tempera- 
tures of  saturated  steam  in  degrees  C. 

Boiler. 

Cut-off. 

Release. 

Back  pressure. 

Initial. 

Final. 

Pres- 
sure. 

Temp. 

Pres- 
sure. 

Temp. 

Pres- 
sure. 

Temp. 

Pres- 
sure. 

Temp. 

9. 

10. 

11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

1 

12.6 

3i-3 

48900 

150.15 

42449 

144.96 

9355 

97-24 

3680 

73-49 

2 

11.83 

33-65 

46380 

yf8.20 

37773 

140.78 

98.24 

3670 

73-42 

3 

16.50 

33-09 

49938 

151.00 

4I4I5 

148  74 

7722 

92.05 

1919 

58.86 

4 

16.50 

35.26 

48075 

150.00 

23070 

124.00 

8417 

94.40 

1900 

58-25 

5 

16.37 

30.42 

49680 

150.77 

39128 

142.00 

5931 

85.00 

1881 

58.44 

6 

16.50 

32.25 

49706 

38339 

141.30 

5737 

84-33 

2134 

61.15 

7 

15-85 

37-8i 

50255 

152.20 

17458 

115.80 

64S7 

87.  s6 

57-" 

8 

43754 

146.20 

34333 

I37-4° 

11053 

101.89 



Work  in  meter-kilograms  and  corresponding  heat  in  calories. 

At  full  pressure. 

Of  expansion. 

Of  back  press're 

Total,  absol'te 

Real,  indicated. 

| 

Work. 

Heat. 

Work. 

Heat. 

Work. 

Heat. 

Work. 

Heat. 

Work. 

Heat. 

1 
ir> 

19. 

20. 

21. 

22. 

23. 

24. 

25. 

26. 

27. 

28. 

1 

P 

1 

5531-5 

13.01 

7020.5 

16.52 

1787.0 

.205 

I2552 

29-53 

10765 

25-325 

« 

2 
3 

5103.5 
44'5-o 

12.005 
10.39 

6725-5 
6710  o 

15-835 
15-79 

^-782.5 
932-0 

.19 
.19 

"833 
11125 

27.84 
26.18 

10050 
10193 

23.65 
23-99 

1 

4 

6285.0 

14.79 

3930.0 

9.24 

922.0 

•J7 

10215    !    24.03 

9293 

21.86 

| 

5 

33I5-0 

7.80 

6085.0 

M-3i 

912.0 

.14 

9480 

22.  11 

8487 

19.97 

6 

3187.0 

7-50 

5825.0 

J3-70 

1035.0 

•43 

9012 

21.20 

7977 

1877 

.2 

7 

5225.0 

12.29 

3070.0 

7.22 

862.0 

.02 

8295 

I9.51 

7433 

17.49 

"rt 

8 

5000.0 

11.76 

6162.0 

14.50 

5212.0 

12.26 

11162 

26.26 

5950 

14.00 

5 

306 


THERMODYNAMICS  OF   THE  STEAM-ENGINE. 


TABLE  XIII. 
RESULTS  OF  EXPERIMENTS  ON  SIMPLE  EXPANSIVE  ENGINES. 


<u 

*tS 

o    • 

Absolute 

Horse- 

3 0 

3 

Bj 

pressures  in 

power. 

kilos,  per 

Cheval  a 

cL2 

Name 
of 

Date. 

Condition. 

a 
1 

£| 

square 
meter. 

vapeur. 

|o 

Engine. 

SG'O 

o 

gj 

ti 

T3 

*°   0 

3 

"o 

33 

jj 

J 

I 

*£ 

i 

IP 

3 

,5 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

1 

2 
3 
4 
5 

6 

7 
8 

10 
11 

Him 
Corliss 

Nov.  18,  1873 
Nov.  28,  1873 
Aug.  26,  1875 
Aug.  27,  1875 
Sept.    7,  1875 
Sept.   8,  1875 
Sept.  29,  1875 
Oct.  28,  1875 
1878 
1878 
1878 

Superheated,  231° 
Saturated 
Superheated,  215° 
*Superheated,  223° 
Superheated,  195° 
Saturated 
t  Superheated,  220° 
J  Superheated,  220° 
Saturated,  jacketed 
Saturated,  jacketed 
Saturated,  jacketed 

30.1736 

30-5494 
29.969 
30.306 
29.98 
30-41 
30-13 
30.00 
50.41 
51-12 
49-34 

0.2570 
0.2570 
0.2139 

0-4539 
0.1628 
0.1628 

0-4539 
0.2867 

A 

48900 
46380 
49938 
48075 
49680 
49706 
50255 
43754 

3680 
3670 
1919 
1900 

1881 
2134 
1759 

1480 
1690 
1840 

144.36 
136.46 
35-77 

13.08 
07.81 
99-53 
78.30 
05 

11 

114.0 

102.0 

95-0 

92 
125 
142 

8.3 

8"-9 
9-7 
ii.  8 
10.4 

46.7 

IO.O 

8.8 
8.1 

*  Throttle-valve  partly  closed.        t  Valve  nearly  closed.        J  Non-condensing. 


Consumption  of  equiv- 
alent dry  saturated 
steam  per  horse-power 
per  hour,  kilos. 

Per  cent  of  water 
in  mixture  in  the 
cylinder. 

Exchange  of  heat  in  per  cent  of  total  heat 
furnished  per  stroke. 

i 

0 

*O  4) 

O    > 

i 

•j 

ij 

*x 

*§• 

•"T  8 

•a  3.2 

li. 
3    • 

|» 

c 

•oS 

S| 

IT 

.c 

Is. 

.C  ^ 

(j 

3 

c  w 

?*q 

«S 

0 

•§  a 

j^e 

—  £ 

11 

•3  i 
c  52 

S| 

3 
o 

1 

?"8 

i!  o 
c  ^ 

|  =  1 

0  Jti 

8* 

.S| 

1 

£'^ 

|c 

£a 

Is 

I* 

* 

? 

M 

^^ 

rtw 

^ 

pi 

Qe 

^ 

^r 

1" 

11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

1 

7.000 

7-633 

8.207 

6.50 

12.  OO 

4-9 

II.  0 

2.0 

7.8 

.2 

—0.40 

16.61 

2 

8.449 

9-307 

10.341 

30.40 

25.20 

9-4 

23-9 

7-3 

15-4 

.O 

0.25 

37-53 

3 

6.7599 

7-3691 

0.38 

I7-50 

7-9 

9-7 

•  4 

S-2 

17.60 

4 

8.655 

t  —  1.50 

"3  .  ii 

10.  5 

0 

0.30 

20.34 

6 

6*655 

7-37° 

V  •  5  J  *• 

8.188 

24.64 

I3.2O 
21.38 

8.10 

22.4 

8.4 

12.5 

.6 

0.05 

18.80 

6 

7.822 

8.837 

9  -.929 

36.00 

35-19 

10.63 

28.3 

5-o 

21.6 

•5 

—0.20 

37-02 

7 
8 

^7.763 

8.663 
12.315 

9  844 

2.52 

12.00 

I5.85 

Dry. 

I.IO 

Dry. 

14.2 

—  1.2 

.6 

3-20 

21.90 
-1.84 

9 

7!i88 

7-983 

9.071 

38.30 

21.70 

26;4 

17.5 

12-3 

^65 

5-  J 

1.9 

II.  21 

10 

7-236 

7-939 

8.724 

19.20 

21.  I 

15-0 

9.8 

•3 

4-9 

1.2 

11.14 

11 

7-307 

7-955 

8.646 

25-30 

18.50 

15-4 

10.4 

8.0 

.1 

4.1 

I.I 

ii.  IS 

*  Superheated  steam  per  horse-power  per  hour.       t  Superheated. 


HIRN'S  ANALYSIS.  307 

gine,  is  calculated  twice,  in  a  memoir  presented  in  1877,  and 
again  in  one  presented  in  1878.  There  are  some  differences 
in  the  two  methods,  and  some  of  the  others  show  discrepancies 
that  do  not  appear  to  be  readily  explained.  In  the  tables 
given  I  have  adhered  to  the  earlier  calculation,  where  the 
entire  data  are  given. 

CALCULATION  OF   TEST  ON   HIRN   ENGINE,    Sept.  7,  1875. 

Volume  of  cylinder,  including  clearance  at  one  end,  0.490  cu.  m. 

Specific  heat  of  superheated  steam,  cp  =  0.5 

Calories- 
Heat  brought  by  dry  vapor  in  cylinder,  0.224  (606.5  +  0.305  X  150.77)  =  146.15 
Heat  brought  by  superheat,  0.5  X  0.224  (IQ5-5  —  150.77)  =  5.01 

Total  heat  brought  to  cylinder,  151.16 

Heat  carried  away  by  condensed  water,  0.224  X  30.42  =      6.81 

Difference,  available  heat,  144-35 

Heat  absorbed  by  condensing  water,  8.7384  (30.42  —  16.37)  =  122.77 

Difference,  21.58 

Heat  equivalent  of  external  indicated  work,  IQ-97 

Heat  lost  by  radiation,  etc.,  2.5          22.47 


—  0.89 

Per  cent  of  error,  HPj_J?  _  _  orf  £t 

151.16 

The  consumption  of  dry  saturated  steam  per  stroke,  calculated  from  the 

151.16 

total  heat,  is  -z =  0.^2317. 

652.48 

The  indicated  horse-power  is     2  X  8487  X  29.98  _ 

60  X  75 

The  net  horse-power  is  113.08  X  0.90  =  102. 

The  consumption  of  dry  saturated  steam  per  horse-power  per  hour  is  : 

Total  horse-power,  0.2317X60X60X75  =     ^      . 

9400 

indicated  horse-power,  °'2317  X  6°  X  6°  X  75  =  7.*37o ; 

8487 

net  horse-power,  7-37Q  =  8  *i88« 

0.90 


308  THERMODYNAMICS  OF   THE  STEAM-ENGINE. 

Weight  of  mixture  of  steam  and  water  in  the  cylinder,  0^.2240 

Weight  of  dry  steam  at  cut-off,  0.1628  X  0.490  X  2.116  =  0.1688 

Weight  of  steam  condensed  during  admission,  =  0.0552  =  24^.6 

Heat  yielded  during  condensation,  0.0552  X  506.5  =  27^96 

Weight  of  dry  steam  at  end  of  stroke,  0.490  X  0.3595  =  0^.1761 

Weight  of  water  in  mixture,  =  0.0479  —  21^.38 

Internal  heat  at  cut-off,  0.1688  X  462.684-0.224  X  143.26  =  110.22 

Internal  heat  at  end  of  stroke,  0.1761  X  507.77  -f-  0.224  X  85.32    =  108.56 


Difference,  1.66 

Heat  furnished  by  superheat,  (195.5  —  142)0.5X0.224=      5.99 

Heat  furnished  by  condensation  during  admission,  27.96 

Sum,  35.61 

Heat  absorbed  by  work  of  expansion,  14.31 

Heat  lost  by  radiation,  etc.,  2.50         16.81 

Qc,  the  heat  rejected  by  the  walls  to  the  condenser,  =    18.80- 

In  per  cent  of  total  heat  received,  Qc  =  — '- —  =  12^.5. 

Internal  heat  at  the  end  of  the  stroke, 
Heat  equivalent  of  work  of  back  pressure, 
Heat  carried  away  by  condensed  water, 


Heat  acquired  by  condensing  water, 

Difference  Qc,  =    i8.8S 

T  ft    ft  ft  T  ft    ft/"k 

Error  in  determination  of  Qc  =  —  —  =  0^.05. 

Heat  yielded  by  0^.224  dry  steam  in  condensing, 

0.224  (624.32  —  30.42)  =  133^.03 
Heat  acquired  by  condensing  water,  =  122.77 


10.26 


Weight  of  water  contained  — ^ —  =  cK.oiSi*  =  °>O1  — ^  =  8£  i 
565.75  0.224 


From  the  quantities  already  calculated,  the  two  remaining  quantities  Qa  and 
Qb  may  be  found  ;  Qd  is  considered  to  be  zero. 

Heat  furnished  by  condensation  during  admission,  27^.96 

Heat  furnished  by  superheat,  5.99 

G»>  =    33-95- 


HIRN'S  ANALYSIS.  309 

Heat  equivalent  of  work  of  expansion,  14  .31 

Internal  heat  at  cut-off  minus  internal  heat  at  end  of  stroke,  1.66 

Qb  =    12.65 


Hallauer's  Tests  on  Compound  Engines.  —  Table  XIV 
gives  the  results  of  experiments  made  on  stationary  compound 
engines  of  different  types.  Experiments  1—7  were  made  on  a 
vertical  Woolf  beam  engine  working  at  Munster.  It  had  the 
two  cylinders  side  by  side  acting  on  the  same  end  of  the  beam, 
the  small  cylinder  nearer  the  columns  so  that  it  had  a  shorter 
stroke.  Both  cylinders  were  jacketed  with  steam  brought 
from  the  boiler  in  a  special  pipe.  The  engine  was  normally 
controlled  by  a  throttle  governor,  but  during  the  experiments 
the  governor  was  disconnected,  and  the  engine  was  run  coupled 
with  another  engine  which  controlled  the  speed.  Experiments 
8  and  9  were  made  on  a  horizontal  Woolf  engine  having  the 
small  cylinder  above  the  large  one,  and  inclined  at  a  small 
angle,  so  that  both  pistons  acted  on  one  crank.  Both  cylin- 
ders were  jacketed  with  the  steam  passing  from  the  boiler  to 
the  small  cylinder  —  a  method  that  cannot  be  recommended, 
since  the  condensation  in  the  jacket  makes  the  steam*  moist  as 
it  enters  the  cylinder.  Experiments  10-13  were  made  on  a 
double  vertical  Woolf  engine  coupled  to  the  same  shaft  ;  10 
and  12  were  made  on  the  left  engine,  and  n  and  13  were 
made  on  the  right  engine.  The  engine  was  controlled  by  a 
governor  which  varied  the  cut-off  of  the  small  cylinder.  The 
cylinders  were  jacketed  with  the  steam  passing  to  the  small 
cylinders.  Experiment  14  was  made  on  a  vertical  Woolf  beam 
engine,  working  at  Saint-Remy. 

Tests  on  Marine  Engines.  —  Table  XV  gives  the  results 
of  experiments  on  various  marine  engines.  Since  the  weight 
of  the  circulating  water  could  not  be  determined,  the  check  on 
the  calculation  of  Qc  could  not  be  obtained. 

Experiments  I,  4,  and  5  are  entered  twice  in  the  table,  —  the 
first  time  as  calculated  with  the  data  given  by  the  experiments, 
and  the  second  time  with  modified  data  which  give  more  con- 


3io 


THERMODYNAMICS  OF   THE  STEAM-ENGINE. 


TABLE  XIV. 
RESULTS  OF  EXPERIMENTS  ON  STATIONARY  COMPOUND  ENGINES. 


Absolute 

C 

v 

. 

pressures, 

Horse- 

'w*U 

* 

3 

| 

kilos. 

power. 

55 

1 

c 

• 

per  sq.  m. 

X 

Place. 

Date. 

Dimen- 

& 

0. 
K 

uv 

a| 

sions. 

en 

V 

J-T3 

En  S 

"1*0 

3 

.2 

vi  u 

| 

£ 

o  J> 

"o 

1 

3 

^ 

PQ 

P 

•5 

c 

1 

I1 

1 

3 

Munster. 

u 

Sept.  21,  22,  1876 
June  20,  21,  1876 
Oct.  24,  25,  1876 

High-pres- 
sure, diam. 
om-55,  stroke 

25-3 
25-0 
25.6 

180.23 
246.92 
284  28 

.... 

22.  92 

51670 

4 

M 

Oct.  17,  18,  1876 

im.4i5.  Low- 

25-1 

346.39 

i9-6o> 

5 
6 

7 

8 
9 

{Factory, 
Dollfus, 
Mieg&Cie 

June  12,  13,  1877 
une  21,  22,  1877 
uly  4,  5,  1877 

Nov.,  1876 

pressure, 
diam.  im.2oo 
stroke  2m.oo, 
Diameter, 
h.  p.  om.38i, 
l.p.  om.8575, 
stroke,  1.297 

25-4 
25.2 

25-25 

39-37 
39-37 

6 
6 

42369 
51670 
56837 

49600 
38380 

2930 

253° 
2950 

185.75 

267.85 

347  -16 

130 

181 

112.08 
161.00 

24.10 
20.52 

17-43 

20.06 

10 

Malmer- 

1877 

26.2 

28 

56837 

1810 

143.11 

118.38 

18.6 

11 

spach. 

25-93 

25 

56837 

175° 

!49-53 

124.74 

12 

" 

M 

25-47 

13 

58903 

2260 

215-7 

185.69 

_    • 

13 
14 

Saint-Remy 

.... 

24.83 
24.503 

13 
19 

58903 
32220 

2180 

212.92 
i37-oo 

183.67 
107.88 

14.9 
9-9 

Ratio  cyls. 

15 

Woolf* 

.... 

0.147 

25 

0.131 

2690 

367 

.... 

T5-7 

16 

" 

.... 

0.147 

25 

0.131 

.... 

1760 

178 

20.  o 

17 

" 

.... 

0.182 

25-5 

0.0778 

2150 

220 

.... 

14.7 

18 

bt 

0.182 

26.0 

0.0385 

1730 

15° 

17.0 

19 

Compound. 

0.348 

88.5 

0.132 

78.5 

17.6 

*  Kind  of  engine. 


Consumption  of  equiv- 
alent dry  saturated 

Per  cent  of  water. 

Exchange  of  heat  in  per  cent  of  total 
heat  per  stroke. 

steam  per  horse-power 

t! 

be 

ho 

, 

per  hour,  kilos. 

O 

• 

c 

g 

o5 

G 

a 
| 

1. 

II 

JB 
1. 

II 

y 

0 

*! 

rt 
1 

.a1 

•a 

Irf 

u 

E  ; 

•o 

i 

Itt   4J 

§"& 

ife 

.Q    *" 

V  V 

c  g 

>> 

—  *j 

•E   D 

•*.!J 

P 

IS. 

•111 

£  *» 

1* 

*a 

|S 

2-2 
3£ 

*j  U 

P 

w-o 
0.2 
*o  >> 
c  y 

[1 

Xi  ft 

< 

II 

11 

U 

*d 

|-2 

-^Jd 
I* 

11 

0  « 

H 

c 

& 

£ 

W 

Qa 

Qc 

Qi 

e. 

Si 

QC 

1 

7-6605 

9-9399 

5-5 

16.61 

30.97 

12.52 

8.36 

6.20 

0.24 

1.83 

8.12 

23.74 

2 

7-7434 

9.5619 



5-o 

16.29 

32.06 

10.32 

8.54 

5-90 

0.25 

1.36 

6.63 

30.27 

3 
4 

7.3966 
7.6104 

9.3984 
9.4663 

linn 

5-o 
6.0 

12.09 
16.00 

31.68 
30.43 

13-75 
12.33 

5-25 
7-43 

6.65 

5-45 

0.43 
1.26 

1.23 

0.98 

6.21 

6.25 

38.10 
38-94 

5 

7-3841 

9.7299 

12.411 

2-35 

21.17 

32.18 

7-39 

14.44 

3-50 

3-5 

x.8i 

8-37 

13.48 

6 

6.9452 

8.7390 

IO-357 

14.21 

28.44 

5-39 

8.58 

1.32 

1-32 

1.38 

7.24 

6.65 

7 

7.  II2I 

8.6140 

9.864 

2.8 

16.17 

28.90 

6.60 

IO.  12 

3-38 

3-38 

1.08 

6.80 

21.89 

8 

7.290 

9.120 

10.563 

3-o 

ii  .20 

5-34 

6.43 

x.xg 

O.IO 

2.14 

8.05 

i-95 

9 

7.328 

8.878 

9-975 

3-0 

10.8 

.... 

4-50 

5.56 

0.75 

0-45 

i-59 

6.15 

1.16 

10 

6.731 

8-273 

10.019 

5-o 

40.0 

.... 

17.60 

25-5 

7-8 

1.6 

1.9 

6.7 

J9-34 

11 

0.821 

8.260 

9.898 

5-o 

36.1 

.... 

17.80 

22.7 

8.2 

0.9 

1.8 

6-7 

21.33 

12 

6.878 

8.149 

9.465 

5-o 

23-7 

.... 

17.90 

I3-72 

8.40 

3-7 

1.23 

5-94 

31-44 

18 

6.983 

8.210 

9-5I7 

5-o 

24-7 

.... 

19.5 

14-43 

9.90 

1.6 

1.20 

5.96 

37.80- 

14 

6.840 

7     CQT 

9  .702 

3.O 
.u 

15 

7.042 

A 
8-354 

9-4 

*8.9 

9-9 

. 

4-9 

o-7 



. 

33-  r 

16 

7  .  316 

Q  •  '45 

10.8 

10.4 

10.6 

6.4 

O  .  2 

17 

6.883 

8.069 

.... 

23.2 

10.4 

17.8 



10.2 

0.8 

38.9 

18 

6.831 

8.228 



.... 

39-0 

20.  i 

16.4 



9-3 

0.4 

.... 

.... 

24-3 

19 

6.667 

7-376 

29.7 

15-2 

15-9 

4-5 

0.8 

.... 

.... 

1.6 

*  Per  cent  of  water  at  end  of  stroke,  small  cylinder  for  15-18. 


HIRN'S  ANAL  YSIS.  3 1 1 

sistent  results.  In  Experiment  i,  the  steam  at  cut-off  in  the 
small  cylinder  appears  to  have  0.2  per  cent  of  water,  and  at  the 
end  of  it  appears  to  be  dry.  Hallauer  thinks  this  improbable 
even  with  an  efficient  steam-jacket,  since  the  steam  passages 
and  valve  openings  are  large,  so  he  gives  a  recalculation  in  la 
which  augments  the  consumption  by  the  amount  cf 

8.416—  8.170 

—^ — -~Z  —  2.8  per  cent. 
8.416 

In  like  manner,  Experiment  4  appears  to  give  dry  steam  at 
cut-off  of  the  small  cylinder,  and  superheated  steam  at  the  end 
of  the  stroke.  The  modified  results  of  4^  show  augmentation 
of  consumption  of  3.5  per  cent.  From  analogy  the  next  ex- 
periment has  the  consumption  increased  by  1.8  per  cent  in  the 
second  form,  5#. 

To  me,  such  a  change  of  the  original  data  appears  to  be 
questionable,  and  the  modified  results  are  certainly  in  doubt  to 
an  extent  equal  to  the  modification  made.  I  have  given  the 
original  data  the  preference  in  the  table,  but  have  included  the 
modified  results  which  are  used  by  Hallauer  in  his  compari- 
sons with  other  engine  tests. 

Discussion  of  Results. — The  experiments  recorded  in 
Table  XIII  show  clearly  the  effect  of  superheated  steam,  and 
of  a  steam-jacket  on  the  interchange  of  heat  between  the 
steam  in  an  engine-cylinder  and  the  walls  of  the  cylinder  ;  and 
show  the  reason  of  the  economy  resulting  from  these  methods 
of  using  steam. 

When  superheated  steam  is  used,  the  heat  Qa  absorbed  by 
the  cylinder  during  admission  of  steam  is  furnished  in  part  by 
the  superheat,  and  consequently  there  is  less  initial  condensa- 
tion than  when  saturated  steam  is  used.  At  release  there  is 
less  moisture  to  be  evaporated  from  the  walls  of  the  cylinder, 
which  in  turn  reduces  the  amount  of  Qa.  This  is  clearly  seen 
from  a  comparison  of  Experiments  I  and  2,  and  5  and  6,  on  the 
Him  engine.  The  effect  on  the  value  of  Qb,  returned  by  the 
walls  of  the  cylinder  to  the  steam,  is  not  so  well  marked. 
With  the  cut-off  at  £  stroke  (Experiments  I  and  2),  the  use  of 


312 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


TABLE    XV. 
EXPERIMENTS  ON  COMPOUND  MARINE  ENGINES. 


Expansion. 

11 

: 

c 

«s 

o 

I 

| 

«j 

Name. 

Condition. 

c 

0.^ 

It 

J3 

Ii 

B 

o 

•  '""  c 

°* 

a"rt 

.2  v 

3  3 

"o  c 

"8c 

11 

CH    " 

aj 

•»J 

'0.2"^ 

Z2 

>°Q 

u  a 

II 

°.S    1 

"I'S. 

M 

« 

& 

M 

C 

^ 

K 

1 

Duquesne 

j  Throttle  open,  longcut- 

0.519 

0.725 

0.376 

80.83 

8490 

13-5 

2880 

la 
3 

•• 

")      off 
Throttle  closed  partly 
Throttle  closed  further 
Cut-off  shortened 

| 

0.650 

0.321 

59-33 
44-49 
76.67 

3180 
1410 
7200 

21-5 

1590 

I 

** 



* 

.... 

.... 

5 

" 

Cut-off  shortened 

| 

0.550 

0.285 

73«°° 

6360 

II.  I 

2000 

6 

7 

y 

Cut-off  shortened 
Cut-off  shortened 

1 

0.225 

O.  TOO 

0.126 
0.052 

62.49 

46-55 

3900 

1665 

17.7 

22.0 

2460 
1840 

8 
9 
10 
11 

Vienne 

Cigale 
Nievre 
Mytho 

Receiver 
Receiver 
Three  cylinders 

0.317 

0.309 
0.380 
0.282 

0.660 

0.750 

0-499 
0.601 

0.209 
0.232 
0.189 
0.169 

75.00 
90.00 
93.80 
44.48 

6Qo 
205 
740 
590 

13.4 

7-5 
"•3 
16.4 

2l6o 
1780 
2420 

1070 

12 

M 

M 

" 

M 

tfc 

6  1  .40 

1350 

II.  2 

1150 

13 

" 

it 

" 

0.690 

0.194 

73-i6 

22OO 

13-0 

1890 

14 

" 

tl 

" 

0.750 

0.212 

66.00 

2590 

10.2 

l870 

15 

Receiver 

*o.8« 
1.45X0.9 

75.00 

689    63 

Consumption  of 
equivalent  dry  satu- 

Per cent  of  water  in  the 
cylinder. 

Exchange  of  heat  in  per  cent  of 
total  heat  per  stroke. 

rated  steam  per 

horse-power  per 
hour,  kilos. 

Sf  a 

V    , 

o  <3 

.5 
•o 

oj 

i  c 

sf 

|i 

i3  >> 

1  « 

!« 

|| 

1 

tt'l 

£.•-" 

«J  0 

'='>! 

!j 

i  c 

«jj 

s 

?f 

O  "c5  ^ 

°  ^<5 

'S'o 

3-0 

s- 

3  ""v, 

o 

5 

3  ° 

c  w  -o 

^    rt  n-^ 

D^ 

tu 

H) 

CJ  ^ 

H 

Q 

M 

w 

Qc 

a 

ft 

^ 

1 

8.179 

9-405 

O.2 

dry 

7  i 

0.50 

i-57 

•23 

27 

la 

8  416 

9.678 

2.4 

2  .2 

9-3 

1.05 

.20 

I03 

2 

8.744 

10.571 

7-2 

3-8 

12.7 

5-75 

4-05 

•93 

I76 

*5 

8.832 

II  .242 

4.0 

2-7 

II.  0 

3-7 

4-7 

•  .1 

72 

4 

8.114 

9  394 

0.0 

s.  h. 

8.6 

2.9 

2.9 

•4 

138 

4a 

8.411 

9-737 

3-4 

°-3 

11.7 

3-2 

2.8 

•3 

T57 

5 

7-9T5 

8.907 

6.5 

1.8 

14.4 

5-4 

3-3 

.6 

227 

5<T 

8.056 

9.066 

8.0 

3-4 

J5-7 

7-o 

3-3 

.6 

290 

6 

6.861 

8-335 

24.0 

5-4 

18.6 

9-8 

.2 

278 

7 
8 

8.154 
7-5T3 

10  448 

8.675 

49-5 

10.  0 

20.5 
4.6 

19-5 
14.8 

12.  I 

6-7 

1:1 

•4 

•4 

244 
28.8 

9 

7.762 

8.390 

5-4 

3.1 

14.7 

7-2 

4.0 

•4 

7-5 

10 

7.729 

8.710 

23.8 

13-8 

32.6 

18.7 

i  .3 

•4 

71 

11 

7-947 

9-5°4 

27.1 

22.4 

30-5 

21.9 

4-7 

.2 

149 

12 

7-343 

8.263 

22    3 

18.8 

29-5 

20.6 

4.0 

•3 

205 

13 

7-397 

8.510 

l6.4 

15-2 

25-7 

15.8 

2.8 

.6 

221 

14 

9-493 

8-350 

ii.  8 

12.  1 

21.  0 

12.3 

2.5 

•3 

22O 

15 

7.5098 

8.6706 

7-46 

13-74 

5-74 

4-7 

•4 

24.9 

*  Diameters  and  stroke  of  cylinder. 


HIRN'S  ANALYSIS.  313 

superheated  steam  reduces  Qb,  both  as  compared  with  the 
total  heat  applied  and  as  compared  with  the  value  of  Qa ;  on 
the  other  hand,  at  |  stroke  (Experiments  5  and  6),  the  reverse 
is  true. 

It  is  noticeable  that  the  actual  number  of  calories  rejected 
by  the  walls  of  the  cylinder  during  the  exhaust  is  almost 
identical  in  the  Experiments  2  and  6,  when  saturated  steam  is 
used.  The  same  thing  is  true  of  Experiments  9,  10,  and  n, 
made  on  the  Corliss  engine  with  a  steam-jacket  and  using  sat- 
urated steam.  There  is  more  variation  of  the  actual  value  of 
Qc  when  superheated  steam  is  used,  which  may  be  attributable 
to  the  varying  degree  of  superheating. 

A  steam-jacket  reduces  the  heat  rejected  by  the  walls  of 
the  cylinder  during  exhaust  in  a  different  way.  Especially 
when  the  cut-off  is  short,  as  in  the  experiments  gjven  in  Table 
XIII,  the  jacket  cannot  have  much  effect  on  the  initial  con- 
densation, and  almost  all  of  the  heat  taken  by  the  walls  of  the 
cylinder  before  cut-off  is  furnished  by  that  condensation. 
During  expansion  a  very  considerable  portion  of  the  moisture 
previously  condensed  on  the  walls  of  the  cylinder  is  evapo- 
rated— much  more  than  would  be  without  a  jacket ;  and  the 
heat  thus  applied  by  the  jacket  does  work,  though  with  a  re- 
duced efficiency.  During  the  exhaust  the  jacket  furnishes  a 
large  portion  of  the  heat  required  to  evaporate  the  moisture  on 
the  walls  of  the  cylinder  at  release ;  this  heat  from  the  jacket 
is  thrown  away,  and  would  be  entirely  wasted  were  it  not  true 
that  the  walls  of  the  cylinder  are  not  chilled  to  the  same  de- 
gree as  when  the  jacket  is  not  used,  and  that  the  initial  con- 
densation is  thereby  reduced. 

The  comparison  of  Experiment  6  with  Experiment  1 1 
may  be  made  to  illustrate  the  preceding  statements.  In  Ex- 
periment 6,  28.3  per  cent  of  all  the  heat  applied  is  absorbed 
by  the  walls  of  the  cylinder  during  the  admission :  of  this  less 
than  4-  is  returned  during  expansion,  and  f  of  the  heat  is 
thrown  out  as  exhaust  waste.  In  the  nth  Experiment,  15.4 
per  cent  of  the  heat  applied  is  absorbed  by  the  walls  of  the 
cylinder.  The  heat  yielded  by  the  walls  of  the  cylinder  during 


THERMODYNAMICS  OF    THE   STEAM-ENGINE. 

expansion  is  f  of  that  absorbed  during  admission,  and  -J  of  the 
amount  absorbed  is  thrown  out  during  exhaust.  The  excess 
of  the  heat  yielded  by  the  walls  of  the  cylinder  during  expan- 
sion and  exhaust  over  that  absorbed  during  admission,  to- 
gether with  the  heat  lost  by  radiation,  is  the  measure  of  heat 
supplied  by  the  jacket. 

To  sum  up  in  a  few  words  :  It  appears  that  the  use  of  su- 
perheated steam  reduces  the  exhaust  waste  and  consequently 
the  initial  condensation  ;  while  the  use  of  a  steam-jacket,  by 
keeping  the  cylinder  hot,  reduces  the  initial  condensation  and 
increases  the  re-evaporation,  and  consequently  reduces  the  ex- 
haust waste. 

Exact  conclusions  cannot  be  drawn  from  the  comparative 
economy  of  the  Hirn  engine  and  the  Corliss  engine.  Yet  it 
may  be  stated  that  these  experiments  show  a  gain  from  the 
use  of  the  steam-jacket  of 


and  a  gain  from  the  use  of  superheated  steam  of  ^ 


A  comparison  of  Experiments  I  and  2  shows  a  gain  from 
superheating  of 

9.307- 


> 

9-307 

Hallauer,  in  estimating  the  gain  from  the  use  of  superheated 
steam,  uses  the  actual  consumption  of  superheated  steam  and 
of  moist  steam,  instead  of  the  equivalent  dry  saturated  steam, 
claiming  that  the  superheating  was  done  by  waste  gases  be- 
yond the  boiler;  but  that  is  evidence  merely  that  the  boiler 
was  not  economical. 

Inspection  of  the  table  shows  that  in  the  three  tests  on  the 
Corliss  engine  the  heat  yielded  by  the  walls  during  expansion 
is  about  |  ,  and  the  heat  rejected  during  exhaust  is  about  -J,  of 
the  heat  absorbed  during  admission.  This,  taken  with  the  fact 


HIRN'S  ANALYSIS.  315 


already  alluded  to,  shows  that  the  action  of  the  walls  was 
nearly  the  same  during  each  of  these  phases,  while  the  cut-off 
changed  from  -^  to  \  of  the  stroke. 

Before  leaving  these  experiments,  attention  should  be 
called  to  the  fact  that  in  the  tests  on  the  Hirn  engine  the  per 
cent  of  moisture  or  priming  in  the  exhaust  steam  has  been  cal- 
culated from  the  weight  and  temperatures  of  the  injection- 
water  in  the  usual  calorimetric  method.  The  per  cent  of 
priming  varies  with  the  method  of  running  the  engine  in  some- 
thing the  same  way  as  does  the  per  cent  of  the  moisture  in  the 
cylinder  at  release  ;  but  it  is  seldom  so  much  as  \  of  the  latter 
quantity,  and  it  is  never  so  great  as  1  1  per  cent.  Attention 
will  be  called  to  this  again  in  connection  with  the  discussion 
of  the  question  whether  the  interchange  of  heat  is  between 
the  steam  and  the  metal  of  the  cylinder,  or  between  the  steam 
and  moisture  remaining  permanently  in  the  cylinder. 

In  examining  the  tests  on  stationary  compound  engines  in 
Table  XIV,  it  is  noticeable  that  while  the  heat  absorbed  during 
admission  is  a  considerable  fraction  of  all  the  heat  applied, 
though  in  most  cases  less  than  with  a  simple  engine,  the  heat 
rejected  by  the  walls  during  exhaust  is  in  all  cases  small,  and  in 
some  cases  it  is  insignificant. 

The  division  of  the  expansion  between  the  two  cylinders  of 
a  compound  engine  with  the  accompanying  division  of  the 
range  of  temperature  reduces  the  amount  of  the  interchange 
of  heat  between  the  steam  and  the  walls  of  the  cylinder,  but 
it  by  no  means  prevents  it.  It  is  possible  to  make  a  calcula- 
tion of  Qb  which  corresponds  to  the  heat  restored  by  the  walls 
of  the  cylinder  during  expansion  in  a  simple  engine  ;  but  here 
that  quantity  represents  a  complicated  change.  During  the 
expansion  in  the  small  cylinder  some  of  the  heat  absorbed  by 
the  walls  of  that  cylinder  before  cut-off  is  restored  ;  during  the 
exhaust  from  the  high-pressure  to  the  low-pressure  cylinder 
heat  is  rejected  from  the  walls  of  the  former,  a  part  of  which 
is  transferred  to  the  walls  of  the  low-pressure  cylinder  by  ini- 
tial condensation  therein  ;  as  the  expansion  goes  on  in  the  low- 
pressure  cylinder,  before  and  after  cut-off  of  that  cylinder,  the 


THERMODYNAMICS  OF   THE   STEAM-ENGINE, 


lowering  pressure  is  accompanied  by  re-evaporation  of  water 
from  its  sides,  and  heat  is  yielded  therefrom.  Consequently 
the  calculation  corresponding  to  the  finding  of  Qb  develops 
positive  and  negative  quantities  whose  sum  is  not  a  measure  of 
the  action  that  actually  takes  place.  The  only  way  of  properly 
investigating  this  action  is  that  suggested  by  the  application  of 
Hirn's  analysis  to  compound  engines  on  page  222,  and  the  data 
for  it  are  not  given  for  these  tests  by  Hallauer. 

The  data  of  the  experiments  on  marine  engines  were  fur- 
nished by  M.  Widman ;  the  results  stated  in  Table  XV  were 
calculated  by  Hallauer.  It  was  not  possible  to  measure  the 
amount  of  cooling  water  used  per  stroke,  consequently  the 
check  given  by  the  condenser  on  the  value  of  Qc  could  not  be 
obtained.  On  the  other  hand,  the  use  of  the  surface  condenser 
gave  a  very  exact  method  of  measuring  the  consumption  of 
steam. 

The  engine  of  the  Duquesne  has  six  cylinders,  arranged  to 
form  three  Woolf  engines,  with  the  small  cylinder  of  each 
above  the  large  cylinder.  From  the  positions  of  the  cylinders 
the  intermediate  receiver  had  a  considerable  volume.  Two 
series  of  experiments  were  made:  I,  2,  and  3  show  the  effects 
of  throttling  the  steam,  and  1,4,  5,  6,  and  7  show  the  effect  of 
shortening  the  cut-off.  Hallauer  has  modified  the  results  in  a 
manner  already  alluded  to  and  has  used  the  second  results  in 
his  comparisons. 

Experiments  I  and  ,3,  Table  XV,  and  15  and  16,  Table 
XIV,  are  compared  in  the  following  table : 


Duquesne. 

Diff. 

Woolf. 

Diff. 

Indicated  horse-power    .... 

1410 

8490 
20100 

2.4 
2.2 

9-3 

8.416 

9-405 
1.9 

1.6 
0-5 
i-7 

0.416 

1-837 
1.8 

I78 
g.IO 

10.8 
10.4 
10.6 

7.316 

9-145 
6.4 

367 
3010 
9-4 

8.Q 

9.6 

7.042 

8.354 
4-9 

1,4 

i-5 

0.7 

0.274 
0.791 
i-5 

Reduction  of  pressure  by  throt- 
tlinjr 

Percentage  of  water: 
Small  cylinder  cut-off 

4.0 
2.7 
II.  0 

8.832 
11.242 
3-7 

Small  cylinder  release  ...... 

Large  cylinder  release  

Consumption  in  kilos: 
Total  horse-power.  

Indicated  horse-power        .  . 

Heat  rejected  to  condenser.  . 

HIRN'S  ANALYSIS.  317 

Hallauer  considers  the  parallelism  exhibited  by  this  table 
to  be  a  verification  of  the  tests  on  the  marine  engine,  in  de- 
fault of  the  check  afforded  by  measuring  the  cooling  water. 

The  interchange  of  heat  between  the  walls  of  the  cylinder 
and  the  steam  is  roughly  indicated  by  the  per  cent  of  water  in 
the  cylinder  at  the  several  points  indicated.  In  the  first  four 
experiments,  where  the  power  is  varied  by  throttling,  these 
percentages  and  the  value  of  Qc,  rejected  to  the  condenser, 
vary  in  an  irregular  manner  and  to  a  small  amount  only.  On 
the  other  hand,  the  increase  of  these  several  quantities  is 
marked  and  regular  when  the  power  is  regulated  by  shorten- 
ing the  cut-off.  It  is  also  apparent  that  the  consumption  is 
reduced  by  increased  expansion  as  far  as  to  eight  expansions, 
though  the  ratio  of  the  volumes  of  the  cylinders  is  ill  adapted 
to  large  expansion,  and  that  it  increases  rapidly  for  more  than 
eight  expansions. 

The  performance  of  the  engine  of  the  Duquesne  with  a 
variable  cut-off  may  be  compared  with  the  stationary  Woolf 
engine,  Table  XIV,  Experiments  17  and  18.  For  example,  the 
marine  engine,  when  exerting  3900  horse-power,  with  8  expan- 
sions, has  9.8  per  cent  for  the  value  of  Qc,  while  the  stationary 
engine,  exerting  220  horse-power,  with  13  expansions,  has  Qc  = 
10.2  per  cent.  Again,  compare  the  consumption  per  total 
horse-power  of  the  marine  engine,  when  exerting  1665  horse- 
power with  20  expansions,  with  that  of  the  stationary  engine 
exerting  1 50  horse-power  with  26  expansions.  The  latter  has 
the  advantage  by 

8.154  —  6.831 


8.154 


=  0.162. 


Of  course  some  of  this  may  be  attributed  to  the  greater 
degree  of  expansion  of  the  latter,  but  the  real  explanation  is 
to  be  sought  in  the  methods  of  obtaining  the  expansion.  The 
ratio  of  the  cylinders  for  the  stationary  engine  is  I  :  5^,  and  the 
expansions  in  the  small  cylinder  are  5.  On  the  other  hand, 
the  ratio  of  cylinders  for  the  marine  engine  is  I  :  2,  and  the 
expansions  in  the  small  cylinder  are  10.  This  large  degree  of 


318  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

expansion  in  the  small  cylinder  of  the  marine  engine  causes  an 
initial  condensation  of  49  per  cent,  while  that  of  the  stationary 
engine  is  39  per  cent. 

The  test  19,  in  Table  XIV,  is  remarkable  for  the  small  con- 
sumption of  steam  per  horse-power  per  hour,  though  the  total 
horse-power  was  only  78.5.  This  engine  was  a  portable  com- 
pound condensing  engine,  having  a  distribution  slide-valve  and 
an  independent  cut-off  valve  for  the  small  cylinder,  and  a  plain 
slide-valve  for  the  large  cylinder.  In  1878  a  medal  was  offered 
by  the  Societe  Industrielle  de  Mulhouse  for  the  first  compound 
engine  constructed  in  Upper  Alsace,  that  should  give  one  brake 
horse-power  (cheval  a  vapeur)  for  less  than  9  kilograms  of  steam. 
This  engine  was  offered  for  trial,  and  was  tested  by  a  committee 
and  awarded  the  medal. 

Isherwood  *  gives,  on  page  319,  the  table  of  data  and  results 
of  tests  transferred  to  the  English  system  of  units. 

Mair's  Steam-engine  Tests. — In  Table  XVII  are  given 
the  data  and  results  of  a  number  of  tests  on  large  engines  of 
various  types,  reported  by  Mr.  George  Mair,f  together  with  a 
very  complete  analysis  according  to  Hirn's  method. 

In  all  of  these  tests  the  power  was  measured  by  indicators 
that  were  tested  after  every  trial,  and  diagrams  were  taken  at 
intervals  of  15  or  20  minutes,  which  were  measured  by  a  planim- 
eter.  The  mechanical  equivalent  of  heat  was  assumed  to  be 
772  foot-pounds  for  facility  in  use  of  tables  of  the  properties 
of  steam,  though  reference  is  made  to  Joule's  later  determina- 
tions. 

The  steam  consumption  was  determined  by  measuring  the 
feed-water  supplied  to  the  boiler.  The  steam  condensed  in  the 
steam-jackets  was  collected  and  weighed  separately.  The  air- 
pump  discharge  was  allowed  to  flow  through  an  orifice  under  a 
measured  head  ;  the  coefficient  of  discharge  for  the  orifice  was 
determined  by  direct  experiments.  The  per  cent  of  priming 
in  the  steam  was  determined  by  calorimetric  tests.  In  the  test 

*  Journal  Franklin  Inst.,  vol.  cxx.,  Oct.  1885. 

f  Proc.  of  the  Inst.  of  Civ.  Engs.,  vol.  Ixx.  page  313,  and  vol.  Ixxix.  page 
323. 


HIRN'S  ANALYSIS. 

TABLE   XVI. 
EXPERIMENTS  ON  A  CONDENSING  COMPOUND  ENGINE. 


319 


July  7,  1879. 
Morning. 

July  7,  1879. 
Afternoon. 

July  8,  1879. 
Morning. 

July  8,  1879. 
Afternoon. 

TOTAL  QUANTITIES. 

2.99889 
16014. 
3951. 
73821. 

91.78 

4.00139 
21253. 

5379- 
98621. 

91.52 

3.00222 
16211. 
3248. 
74039. 

91.69 

1.81 

Wide°open. 
0.25 
0.98 
o  925 

0-45 
0.91 

0.75 
9.64 
14.22 

48.0 
86.9 

99.8 

33-4 
35-3 
34-8 
27.8 

34  -5 
21.  16 
9.6 
3-8 
2.4 
17.0 

23.1 
40.7 
63.9 

55-7 

16.9 

19.4 
19108. 
21906. 

3.24139 

17253- 
4265. 
78894. 

92.16 

1.91 

88.7 
Wide  open. 
0.42 
0.98 
0.925 
0-45 
0.91 

°-75 
6.26 
14.22 

48.0 
96.7 

103.0 
91-5 
45-2 
46.4 
42.6 
30-7 

43-2 
27.7 

12.6 

3-8 
2.4 
22.3 

25-1 
52-7 
77.8 
67-5 

16.9 

19.5 
18924. 

21804. 

Pounds  of  feed-water  pumped  into  the  boiler 

ENGINE. 
Steam-pressure  in  boiler  in    pounds   per 
square  inch  above  the  atmosphere  

Pressure   in   the  condenser  in  pounds  per 
square  inch  above  zero  

Number  of  revolutions  per  minute  

89. 
Wide  open. 
0.42 
0.98 
0.925 

0-45 
0.91 

1:11 

14.22 

48-3 
95-7 

100.8 

89.3 
44.1 

45-3 
41.6 
30.2 

43-o 
27.5 
12.3 
3-8 
2.4 

22.1 

24.8 
52.4 

77.2 
67.7 

17.7 

i9-S 
19110. 
21785- 

88.5 
Wide  open. 
0.42 
0.98 
0.925 

°-45 
0.91 
o-7S 
6.26 
14.22 

48.1 
97-7 

102.5 
91  .0 

3:! 

42.4 
30.8 

43-2 
27.7 
12.5 
3-8 
2.4 
22.3 

25.2 
52.5 
77.6 
67-5 

17.8 

19.9 

i935i. 
21960. 

Cut-off,  small  cylinder  

Cut-off  large  cylinde'r  

Number  of  times  the  steam  was  expanded.  . 
Atmospheric  pressure  in  pounds  per  sq.  inch 

TEMPERATURES. 
Temperature  in  degrees  Fahrenheit  of  the 
condensing  water  when  admitted   to  the 

Temperature  in  degrees  Fahrenheit  of  the 
condensing  water  and  water  of  steam  con- 
densation when  taken  from  condenser  

ABSOLUTE  STEAM-PRESSURES  IN  SMALL 
CYLINDER  PER  INDICATOR. 
At  commencement  of  stroke    

End  of  stroke  

Mean  back  pressure 

At  compression  

Indicated  pressure               .       . 

ABSOLUTE  STEAM-PRESSURES  IN  LARGE 
CYLINDER  PER  INDICATOR. 
At  commencement  of  stroke    

Point  of  cut-off 

End  of  stroke  

Mean  back  pressure 

At  compressipn  

Indicated  pressure  

HORSE-  POWER. 
Indicated     horse-power   developed    in  the 
small  cylinder     

Indicated    horse-power   developed    in    the 
large  cylinder  

Aggregate   indicated   horse-power    devel- 
oped by  the  engine  

Horse-power    developed   by  the  engine    at 
the  friction-brake 

ECONOMIC  RESULTS. 
Pounds  of  feed-water  per  hour  per  indi- 
cated horse-power  

Pounds  of  feed-water   per  hour  per  brake 
horse-power  

Fahrenheit  units  of  heat  per  hour  per  indi- 
cated horse-power  

Fahrenheit  units  of  heat  per  hour  per  brake 
horse-power  

320  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

C  the  condensation  in  steam-pipe  was  drained  into  buckets  and 
weighed  ;  in  the  test  B  the  condensation  in  the  steam-pipe 
flowed  to  the  engine,  and  an  allowance  was  made  depending  on 
the  condensation  caught  during  the  test  C.  In  all  the  other 
tests  the  steam-pipes  drained  toward  the  boilers. 

The  test  A  was  made  on  a  single  cylinder  rotative  pump- 
ing-engine,  having  a  diameter  of  45  inches  and  a  stroke  of  5 
feet  6  inches.  The  sides  and  ends  of  the  cylinder  were  jack- 
eted with  boiler  steam.  The  steam  was  distributed  by  sepa- 
rate slide-valves  near  the  ends  of  the  cylinder,  with  expansion- 
plates  adjustable  by  hand,  on  the  backs  of  the  main  valves.  A 
surface  condenser  was  used.  Three  tests  were  made  on  this 
engine,  each  of  which  gave  the  same  result ;  one  test  only  is 
therefore  given  in  the  table.  The  engine  had  been  at  work 
nine  months  when  tested  ;  it  was  carefully  examined,  and  the 
piston  and  valves  were  tight  and  in  good  order. 

The  tests  B  and  C  were  made  on  a  Woolf  beam  rotative 
engine,  working  a  deep-well  pump  direct  from  the  beam,  which 
had  been  working  six  months  when  tested.  The  cylinders 
were  22  inches  in  diameter  by  3  feet  7  inches  stroke,  and 
34  inches  diameter  by  5  feet  6  inches  stroke,  and  were 
jacketed  with  boiler  steam  on  the  sides  and  ends.  The  steam 
was  distributed  by  a  long  slide  with  equilibrium  passages  in  it, 
and  expansion-plates  on  the  back,  worked  by  eccentrics ;  there 
was  a  jet  condenser,  and  the  air-pump  discharge  was  measured. 
Two  tests  were  made — one  with  and  one  without  steam  in  the 
jackets. 

The  tests  D,  E,  and  F  were  made  on  a  Woolf  beam-engine 
driving  a  flour-mill.  The  cylinders  were  24^-  inches  in  diame- 
ter by  3  feet  5  inches  stroke,  and  38  inches  diameter  by  5  feet 
6  inches  stroke,  and  were  steam-jacketed  on  the  sides  only. 
The  steam  was  distributed  to  the  high-pressure  cylinder  by  a 
slide-valve  with  cut-off  plates  on  the  back,  and  to  the  low-pres- 
sure cylinder  by  a  piston-valve,  all  being  worked  by  eccentrics. 
The  steam  was  condensed  in  a  surface  condenser.  Three  tests 
were  made — two  with  and  one  without  steam  in  the  jackets. 

The  tests  G  and  H  were  made  on  an  unjacketed  horizontal 


HIRN'S  ANALYSIS. 


321 


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HIRN'S  ANALYSIS.  325 

Woolf  engine,  of  a  type  very  commonly  used  in  factories  in 
Lancashire.  The  cylinders  were  15!  and  28 J  inches  in  diame- 
ter by  4  feet  3  inches  stroke.  The  piston  speed  was  about  680 
feet  per  minute  and  the  load  was  light,  so  that  the  steam  was 
much  wire-drawn.  Three  trials  were  made,  during  which  the 
boiler-feed  and  air-pump  discharge  were  measured  ;  the  first  test 
was  not  reported,  as  the  engine  was  stopped  during  the  test. 

The  test  I  was  made  on  a  compound  beam  receiver  engine 
with  the  cranks  at  right  angles,  working  pumps  directly  from 
the  beams.  The  cylinders  were  21  and  36  inches  in  diameter, 
and  the  stroke  was  5  feet  6  inches.  Both  cylinders,  with  the 
exception  of  the  high-pressure  cylinder  and  the  receiver-covers, 
were  jacketed  with  boiler  steam.  The  steam  was  distributed 
by  slides,  one  at  each  end  of  each  of  the  cylinders,  with  cut-off 
plates  adjustable  by  hand.  A  jet  condenser  was  used,  and  the 
air-pump  discharge  was  measured.  Two  tests  were  made,  giv- 
ing the  same  result,  so  that  only  one  was  reported. 

The  test  K  was  made  on  a  Cornish  engine  working  a  single- 
acting  piston  pump  direct  from  the  beam,  and  having  the 
usual  Cornish,  double-beat,  steam,  equilibrium,  and  exhaust- 
valves,  a  single-acting  air-pump,  and  a  jet  condenser ;  the  cyl- 
inder was  68^  inches  in  diameter  by  8  feet  stroke,  and  was 
jacketed  on  the  sides  with  boiler  steam.  The  pump  delivered 
its  water  on  the  up  or  steam  stroke,  so  that  the  preponderance 
of  weight  on  the  pump-pole  was  only  enough  to  overcome 
the  suction  lift.  The  valves  and  piston  were  inspected  to  as- 
sure their  tightness  before  the  test.  The  engine  was  doing 
the  highest  duty  at  the  West  Middlesex  Waterworks,  and  was 
taken  as  one  of  the  best  engines  of  its  type  now  working. 
This  type  of  engine  was  developed  in  Cornwall,  where  it  was 
used  to  pump  water  from  deep  mines  by  a  pump-rod  hung 
directly  from  one  end  of  the  beam  while  the  piston  was  hung 
from  the  other  end  of  the  beam.  It  had  no  fly-wheel,  but  the 
pump-rod,  beam,  and  counter-weights  made  in  the  aggregate 
a  large  reciprocating  mass,  that  absorbed  work  during  the  first 
part  of  the  stroke  when  the  steam-pressure  in  the  cylinder  was 
high,  and  restored  that  work  and  assisted  the  steam  to  com- 


326  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

plete  the  stroke  after  it  has  lost  pressure  through  expansion, 
during  the  latter  part  of  the  stroke.  Such  a  reciprocating 
mass  is  essential  to  the  proper  action  of  the  engine  with  a  good 
degree  of  expansion.  The  pumps  of  the  original  engines  were 
worked  by  the  weight  of  the  rods  during  the  return  or  equi- 
librium stroke,  at  which  time  there  was  free  communication 
between  the  two  ends  of  the  cylinder.  The  lower  end  of  the 
cylinder  was  open  to  the  condenser  during  the  steam-stroke. 

The  tests  L  and  M  were  made  on  a  single-cylinder  beam 
rotative  pumping-engine,  having  a  diameter  of  32  inches  and  a 
stroke  of  5  feet  6  inches.  The  cylinder  sides  and  base  were 
jacketed  with  boiler  steam.  Steam  was  distributed  by  slide- 
valves  at  the  top  and  bottom  of  the  cylinder,  with  cut-off 
plates,  adjustable  by  hand,  on  the  backs  of  the  main  valves. 
There  was  a  jet  condenser,  but  the  air-pump  discharge  could 
not  be  measured. 

The  tests  N  and  O  were  made  on  a  single-cylinder  beam 
rotative  engine,  similar  to  the  one  just  described,  and  taking 
steam  from  the  same  boilers.  The  cylinder  was  27  inches  in 
diameter,  by  6  feet  stroke. 

The  test  P  was  made  on  a  Bull  engine  with  a  cylinder  68 
inches  in  diameter  by  10  feet  stroke,  driving  direct  a  45-inch 
plunger-pump,  and  forcing  water  to  a  height  of  40  to  55  feet. 
The  valves  and  gear  were  of  the  usual  Cornish  pattern,  and  the 
sides  and  base  of  the  cylinder  were  steam-jacketed.  This  type 
of  engine  differs  from  the  Cornish  engine  in  not  having  a  beam, 
and  though  the  pump-rod  is  loaded  there  is  seldom  sufficient 
reciprocating  mass  to  allow  of  much  expansion.  In  the  case  of 
the  engine  tested  only  if  expansions  could  be  obtained.  For 
convenience,  the  steam-stroke  is  detailed  under  the  heading  of 
the  high-pressure  cylinder,  and  the  exhaust-stroke  under  the 
heading 'of  the  low-pressure  cylinder. 

The  tests  Q  and  R  were  made  on  a  Woolf  beam  rotative 
engine,  working  a  double-acting  pump.  The  cylinders  were  29 
inches  diameter  by  5  feet  5  inches  stroke,  and  47^  inches 
diameter  by  8  feet  stroke,  and  jacketed  with  steam  on  the  sides 
and  ends.  Steam  was  distributed  by  slide-valves  with  adjust- 


HIKN'S  ANALYSIS.  327 

able  cut-off  plates  to  the  high-pressure  cylinder ;  the  exhaust- 
valves  are  double-beat  valves  worked  by  cams. 

The  interchanges  of  heat  between  the  steam  and  the  walls 
of  the  cylinder  in  these  tests  are  calculated  by  a  process  that 
is  equivalent  to  that  indicated  by  equations  (256)  to  (259).  To 
make  the  matter  clear,  and  to  explain  some  of  the  headings  of 
Table  XVII,  the  entire  calculations  for  the  test  I  are  given 
here. 

The  engine  was  compound,  steam-jacketed,  with  an  interme- 
diate receiver,  and  ran  at  an  average  speed  of  23.98  revolutions 
per  minute  and  expanded  the  steam  13.61  times.  The  absolute 
boiler-pressure  was  76  pounds,  and  the  indicated  horse-power 
127.4.  The  air-pump  discharge  was  25.558  pounds  per  stroke, 
the  initial  and  final  temperatures  being  5O°.o  and  73°-4  F. 

The  weights  of  water  and  steam  per  stroke  were : 

Pounds. 

Boiler  delivery, ,.    ,,  .*.,..,   *    0.69693 

Steam  through  cylinders,      .     .     .     .     MX  =    0.58338 

Priming, M(i  —  x)  —    0.02430 

Condensation  in  jackets, Mj  —    0.08925 

Injection-water, G  =  24.95 

The  heat  brought  into  the  high-pressure  cylinder  of  the  en- 
gine per  stroke  is 

Q  =  Mx\  +  M(i  —  x)q  =  0.58338  X  1 176  +  0.0243  X  278.58 

=  686.06  +  6.76  =  692.82  B.  T.  U., 

in  which  A.  is  the  total  heat  and  q  the  heat  of  the  liquid  corre- 
sponding to  the  pressure  of  the  entering  steam.  Let  r  be  the 
heat  of  vaporization  at  the  same  pressure,  then  the  heat  sup- 
plied by  the  steam-jackets  is 

QJ  +  Q;  =  0.08925  x  897.45  =  80.09 B- T- u- 

The  total  amount  of  heat  delivered  to  the  engine  per  stroke 
is 

Q+Qf+Q/  =  772-91  B.T.U. 


328  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

The  heat  retained  by  the  condensed  steam  at  the  tempera- 
ture /4  of  the  air-pump  discharge  is 


<  -  32)  =  0.60768(73.4  -  32)  =  25.16  B.  T.  U. 
So  that  the  heat  used  by  the  engine  per  stroke  was 
772.91  -  25.16  =  747.75  B.  T.  U. 

The  thermal  units  per  horse-power  per  minute,  calculated 
from  32°  F.,  was 

772.91  X  2  X  revolutions       772.91  X  2  X  23.98 

TTPT-  1  5/T" 

The  number  of  pounds  of  dry  steam  consumed  per  horse- 
power per  hour  was 

772.91  X  2  X  revolutions  X  60  _  772.91  X  2  X  2398  X  60. 
H.  P.  x  A.  127.4  X  1176 

=  14.84  pounds. 

The  actual  number  of  pounds  of  moist  steam  used  per  horse- 
power per  hour  was 

0.69693  X  2  X  23.98  X  60 
—  H_Z£  -  £.2  -  —  I5^  pounds. 
127.4 

Both  of  these  results  show  exceptionally  high  economy  of 
the  use  of  steam  at  an  absolute  pressure  of  76  pounds. 

The  density  of  the  steam  in  the  cylinder  at  different  points 
of  the  stroke  was  calculated  by  aid  of  an  adaptation  of  Zeuner's  * 
formula 

y  =  0.606  1/0-9393, 

which  for  English  units  may  be  written 

log  Y  =  °-9393  log/  -  2.51853- 


*  Mechanische  Warmetheorie,  page  294. 


HIRN'S  ANALYSIS.  329 

At  cut-off  in  the  high-pressure  cylinder,  for  example,  the 
absolute  pressure  was  p^  =  64  pounds  ;  and  the  density,  or 
weight  in  pounds  of  one  cubic  foot,  of  dry  steam  at  this  pres- 
sure, is  by  the  formula  y1  =  0.1506  pounds.  The  volume  of 
steam  at  cut-off,  allowing  for  clearance,  was  2.9161  cubic  feet; 
hence  the  weight  of  dry  steam  at  cut-off  was 

2.9161  X  0.1506  =  0.4392  of  a  pound. 

By  a  similar  calculation  the  weight  of  dry  steam  caught  at 
the  beginning  of  compression  was  found  to  be  0.05913  of  a 
pound.  This  added  to  the  weight  of  moist  steam  per  stroke 
gives  for  the  weight  of  the  mixture  in  the  cylinder 

0.60768  +  0.05913  =  0.66681  of  a  pound. 

Consequently  the  per  cent  of  water  in  cylinder  at  cut-off 
was 

0.66681  —  0.4392 
100  *-       0.66681   '    -=34-  1  per  cent. 

The  heat  equivalents  of  the  intrinsic  energy  of  the  mix- 
ture in  the  cylinder  at  cut-off,  release,  compression,  and  admis- 
sion are  given  by  the  equations 


....     (294) 
....     (295) 
(296) 
70  =  M0(x0p0  +  ?.)  ;   .......     (297) 


in  which  M  is  the  weight  of  moist  steam  through  the  cylinders 
per  stroke,  and  M0  is  the  weight  of  steam  caught  at  compres- 
sion, on  the  assumption  that  the  steam  is  then  dry  and  satu- 
rated ;  and  x  is  the  part  of  one  pound  of  the  mixture  that  is 
steam  ;  and  p  and  q  are  the  heat  equivalent  of  intrinsic  energy 
and  the  heat  of  the  liquid,  at  the  several  points  mentioned. 


330  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

For  the  high-pressure  cylinder  Mr.  Mair  writes 

Qa=Q  +  f*-f>-AWa;    ..",;   ,.".,     .     (298) 

0*  =  /,-/,  +  ^^; (299) 

Qc  =  Qa  +  Gd  +  Qj-Qb-Qe',    .    .    .    (300) 
Qd  =  l.-l.  +  AWb; (301) 

The  equation  for  Qc  is  obtained  by  aid  of  the  equation 

Q.+&+Q,=  &+Q,+Q. (302) 

which  asserts  that  the  heat  absorbed  by  the  cylinder  walls  dur- 
ing adfnission  and  compression,  together  with  the  heat  given 
up  by  the  steam  in  the  high-pressure  jacket,  is  equal  to  the 
heat  yielded  during  expansion  and  exhaust,  plus  the  heat  lost 
by  radiation.  For  the  low-pressure  cylinder  he  gives  the  equa- 
tion 

&+G/+G;  =  &'+o/+ a%  •  •  .  (303) 

which  asserts  that  the  low-pressure  cylinder  walls  receive  the 
heat  Qc  rejected  from  the  high-pressure  cylinder  during  ex- 
haust, the  heat  absorbed  by  the  wall  during  compression,  and 
the  heat  yielded  by  the  steam  condensed  in  the  low-pressure 
jackets,  and  that  this  heat  is  equal  to  that  yielded  by  the  walls 
during  expansion,  during  exhaust,  and  by  external  radiation. 
The  quantity  Qbf  is  that  complex  quantity  described  on  page 
222,  and  it  is  assumed  that  it  applies  to  the  whole  stroke  of 
the  low-pressure  piston,  both  before  and  after  cut-off.  For  the 
low-pressure  cylinder  he  gives 

Qb' •=/,'-(/,_  /,  +  /.'  +  AWt)+  A  Wt';     .     (304) 

<2/  =  &+e/  +  <2/-a'-<2/; (305) 

&r  =  i.'-f:+AW (306) 

Equation  (306)  is  of  the  same  form  as  equation  (250),  and 
equation  (305)  is  obtained  from  equation  (261).  To  find  Qbf  it 
is  assumed  that  the  difference  between  the  heat  equivalents  of 
the  intrinsic  energy  at  release  and  compression  in  the  high-pres- 
sure cylinder  is  thrown  into  the  low-pressure  cylinder,  together 


HIRSTS  ANALYSIS.  331 

with  the  heat  equivalent  of  the  absolute  work  during  exhaust 
from  that  cylinder,  and  that  to  this  sum  is  to  be  added  the 
heat  equivalent  of  the  intrinsic  energy  of  the  steam  at  the 
end  of  compression  in  the  low-pressure  cylinder. 
For  the  test  I  we  have 

Qa  =  692.82  +  33.36  -  540.80  -  37.49  =  147.89  B.  T.  U. ; 

Qb  =  58370  -  540.80  +  54.61  =  97.5 1  B.  T.  U. ; 

Qd  =  63.54  -  33.36  +  7.14  -  37.32  B.  T.  U. ; 

Qe  =  147.89 +  37.32 +  32.43 -97.51 -7.00=  1 13.13  B.T.U.; 

Qb'  =  546.82  -  (583.70  -  63.54  +  17.89  +  31.47)  +  72.69  ; 

=  49.99  B.  T.  U. ; 

Qd'  =  10.60  -  17.89  +  0.60  =  -  6.69  B.  T.  U. ; 
G/  =  II3-I3  -  6.69  +  47.66-49.99-  15.72  =  88.39  B.T.  U. 

The  engine  on  which  test  I  was  made  had  a  jacketed  re- 
ceiver, and  in  this  calculation  as  well  as  in  Table  XVII  the 
condensation  in  the  receiver  jacket  is  added  to  that  in  the  low- 
pressure  jacket,  and  the  radiation  from  the  receiver  is  added  to 
that  from  the  low-pressure  cylinder. 

In  the  table  these  several  quantities  of  heat  are  stated  in 
percentages  of  the  heat  used  by  the  engine  per  stroke,  that  is,  of 

Q+Qj+Qj  -Mqt, 

to  facilitate  the  comparison  of  tests  made  on  different  engines. 
Discussion  of  Results. — The  effect  of  a  steam-jacket  on 
a  single-cylinder  engine  may  be  seen  by  comparing  the  tests 
L  and  M.  With  a  loss  of  only  one  pound  boiler-pressure,  it 
was  found  necessary  to  reduce  the  expansions  from  4.33  to  3.84, 
in  order  to  obtain  the  same  power  without  the  jacket  in  M  as 
with  the  jacket  in  L.  Comparing  the  B.T.  U.  per  horse-power 
per  minute,  the  gain  from  the  use  of  the  steam-jacket,  and  the 
greater  expansion  that  could  then  be  used,  is 

515.9  —  430.0 

100  X  — Z~ —  =  1 6  per  cent. 

515.9 


332  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Comparing  the  interchanges  of  heat  between  the  walls  of 
the  cylinder,  it  appears  that  the  use  of  the  steam-jacket  reduces 
the  heat  Qc  rejected  during  exhaust,  and  consequently  the  ini- 
tial condensation,  as  shown  by  Qa,  while  the  external  radiation 
is  a  little  larger  with  a  jacket  than  without. 

Comparing  the  tests  B  and  C  made  with  and  without  steam- 
jackets  on  a  compound  Woolf  engine,  there  appears  to  be  a 
gain  of 

5I9-5  —  338.8 
100  x  --  5^5"       =  34  per  cent- 

but  this  difference  is  largely  due  to  the  fact  that  in  the  test  C 
the  steam-pipe  was  well  drained,  and  in  the  test  B  it  was  not. 
Comparing  the  tests  E  and  F,  the  gain  from  the  use  of  the 
steam-jackets  and  of  the  larger  expansion  then  possible  is 

378.1  —  341.8 

loo  x  -  --      =  I0£  Per  cent' 


which  would  probably  be  increased  were  the  ends  of  the  cylin- 
ders jacketed  as  well  as  the  sides.  In  this  case,  with  the  larger 
degree  of  expansion  accompanying  the  use  of  the  jackets,  it 
appears  that  the  initial  condensation  in  the  high-pressure  cylin- 
der is  not  greatly  affected,  and  Qa  is  nearly  the  same  in  both 
tests  ;  but  the  heat  restored  during  the  expansion  in  the  high- 
pressure  cylinder  Qb,  and  in  the  low-pressure  cylinder  Qb>,  are 
both  increased,  so  that  Qc',  the  exhaust  waste,  is  reduced  from 
22.4  per  cent  to  9.6  per  cent. 

The  steam  consumption  in  the  test  I  is  remarkably  low, 
showing  an  excellent  adaptation  of  the  engine  to  its  work.  It 
is  interesting  to  compare  the  interchanges  of  heat  in  this  test 
with  those  in  the  tests  T  and  U,  which  give  nearly  as  good  an 
economy,  and  with  other  tests  giving  a  poorer  economy.  It  is 
noteworthy  that  the  exhaust  waste  Qe*  for  the  tests  of  com- 
pound engines  given  in  Table  XVII  cannot  be  regarded  as  a 
measure  of  the  economy  of  the  engine,  neither  can  that  engine 
be  said  to  be  working  under  the  best  conditions  which  shows 


HIRAT'S  ANALYSIS.  333 

in  general  the  smallest  interchanges  of  heat  between  the  steam 
and  the  walls  of  the  cylinder.  The  best  result  appears  rather 
to  be  attained  by  a  judicious  or  fortunate  compromise  of  the 
gain  from  expansion  and  the  loss  from  condensation  and  evap- 
oration, and  of  the  amelioration  of  the  latter  by  the  use  of 
steam-jackets  in  which  heat  is  usefully  applied  for  that  purpose, 
though  with  a  loss  of  thermodynamic  efficiency. 

Institute  of  Technology  Tests. — The  data  and  results  of 
tests  made  on  a  Harris-Corliss  engine  in  the  laboratory  of  the 
Massachusetts  Institute  of  Technology  are  given  in  Table 
XVIII.  This  table  is  given  in  part  to  afford  examples  to  which 
the  equations  for  Hirn's  Analysis  on  page  192  may  be  applied 
by  the  student. 

The  engine  is  an  automatic  cut-off  unjacketed  engine  using 
saturated  steam.  The  stroke  is  24  inches  and  the  diameter  is 
8  inches.  During  the  tests  the  governor  was  disconnected,  the 
cut-off  was  fixed,  and  the  speed  was  regulated  by  another 
engine  coupled  with  this  engine.  Both  the  condensed  steam 
and  the  cooling  water  from  a  surface  condenser  were  weighed 
in  tanks. 

Water  in  the  Cylinder. — As  a  conclusion  of  his  analysis 
applied  to  his  own  and  to  Hallauer's  engine  tests,  Hirn  *  con- 
cludes that  all  the  theories  of  the  steam-engine  proposed  by 
writers  on  thermodynamics,  based  on  the  hypothesis  that  the 
interaction  between  the  steam  and  the  walls  of  the  cylinder 
is  inconsiderable,  are  liable  to  be  in  error  to  the  extent  of 
50  per  cent,  and  are  consequently  entirely  useless  and  mis- 
leading. In  reviewing  these  experiments  and  the  conclu- 
sions from  them,  Zeunerf  developed  the  equations  (256)  to 
(259)  substantially  as  given  on  page  189;  and,  in  addition  to 
pointing  out  that  the  possible  effect  of  eddies  and  mechanical 
motion  of  the  steam  in  general  had  been  neglected,  and  that 
the  method  of  calculation  given  on  page  307  is  inaccurate,  he 
called  attention  to  the  fact  that  a  thin  layer  of  water  adhering 


*  Th6orie  m6canique  de  la  Chaleur,  vol.  ii.  p.  68. 
f  Civil-ingenieur,  xxvii. 


334 


THERMODYNAMICS  OF   THE  STEAM-ENGINE. 


Absolute  pressures,  pounds. 

Admission. 
A 

W 

B 

oo  t*%  0*00  oo 

fO  P?  M    S  M 

w 
y 

OO    tx  OOO  OO 

4-  M    6    ro  « 
«    «    N    PI    « 

Compression. 
A 

H 
SB 

OO    tx  O^OO  OO 

M 

U 

OO    t"s  O^OO  00 

Release, 
/a 

pd 

ad 

00   tx  rooo   O 

>6   ON  6   CO  M 

w 
J 

ro  rx\o  oo  n 

VO    t^.00    M    ON 

-     M     H     «     N 

S'.. 

r 

w 
sd 

<n  t^  »o  «o  ro 

\6  ei  i~-  6  ro 

t^OO    l^OO  CO 

M 

u 

M     (^N     HVO 

t^.  ro  •*  t^.  ro 
txoO    tx  txCO 

•spunod  'a3ni»3      ^ 
Aq  gjnssajd-jailog 

SKSfif;: 

•tpui  ajsnbs  aq}  uo 
spunod  '.lajauiojBg 

oo  r~  o>oo  oo 

Temperatures, 
degrees  Fahrenheit. 

•UJJBM  'J3JBM.         ^ 

-Sutsuapuo3  "** 

ro  O  O  oo  ro 

4^6  t^.  c!  oo 
r^oo  t->  rooo 

•pJOD  'J3JBM         .M 

-J3uisuapuo3  "*» 

»<)  00    M  VO    O> 

o»  T*-  ON  ro  N 
ro  in  ro  10  m 

•CUB3JS          ^. 

pssuapuo3  "** 

VO     10  000    M 

<2  ix  si,  i 

'UJBa-js  ui 
Uuiuiud  jo  }U3D  jbj    1 

.... 

•spunod  'jaiBM-Sui 
-suapuoD  jo  Jq3p'^ 

S??s% 

rog  ^-oo  -j- 

•spunod  'pasn 
raH3js  jo  iqjSpM 

ro  t>-  O  >ooo 
2-ro^^S 

•suonn[OA3j 
jo  jaquinu  imoj. 

O^  O  O  W    N 
r*">  O    r**)  fx  Os 

V^^ 

•sainuioi  'uonBjnQ 

s^ass 

•jaqmnM       |    ^^m^^ 

Interchanges  of  heat. 
B.  T.  U. 

•JOJJ3           « 

f5?Ss 

•uoissajduioo 
JSuunp  SIIBAV      oJ 
Aq  paqaosqy 

00666 

•ismjqxa 
Suunp  s\\vfA.      Q£ 
Aq  pappiA 

T???  r 

VO  00  i    ti.  ON  4- 

•uoisuedxa 
Suunp  SH^AV      <<£ 
Aq  papp;A 

vo  tx  ro  10  M 

•uoissiuipB 
Suunp  SH^M^      Q? 
A'q  paqjosqy 

ONCO    N    S)  JH" 
O    w    M    rp  in 

•raB3;s  ;sioin 
jo  spunod      Qy 

ffl  Ul  }B3fJ 

(M    M    O    ON 

Heat  equivalents  of  work. 
B.  T.  U. 

Compression. 
AW* 

ffi 

?E  ?S  S 

o  o  o  o  o 

W 
U 

S>r^S   ^^ 
O   O    O   O    O 

o  o  o  o  o 

fe 

H 
DC 

ro  O  oo   •«•  r* 
r-.  (N  NO    -r  •*• 

w 
u 

t^  ci    ^t-  O  *O 
co  co  co1co'co> 

Expansion. 
AWb 

M 

ffi 

If!!! 

H 
U 

o-  10  N  f-  rx 

MOM    >OCO 

ro  ro  ro  ro  rn 

Admission. 

*w* 

c4 
ffi 

ONNO    ro  ^  M 
tvco    ro  H   M 

ON  rOvO    CNl    tx 

6   M   M   M   ro 

td 
U 

!?!!! 

Events  of  the  stroke  — 
per  cent  of  stroke  from  beginning. 

i1' 

H 
ffi" 

txVO    ^-0    ON 

W 
U 

«  ro  ON  10  ro 

N     M     O     HI    M 

Release. 

M 

tc 

88888 

U 

88888 

Cut-off. 

D2 

O   IN   O    "0  O 

M 

U 

O    N    O    "TO 

•jaquin^        |     ^.-,t?_.- 

HIRN'S  ANALYSIS.  335 

to  the  walls  of  the  cylinder  and  participating  in  the  changes  of 
temperature,  would  account  for  the  larger  part  of  the  disturb- 
ances attributed  to  the  action  of  the  metallic  walls  of  the  cylin- 
der. It  consequently  becomes  of  great  importance  to  deter- 
mine M0 ,  the  weight  of  the  mingled  water  and  steam  caught  in 
the  cylinder  at  compression.  The  effect  of  the  mechanical 
motion  of  the  steam  in  the  cylinder  during  expansion  cannot 
be  considerable,  and  the  errors  of  the  method  of  calculation 
employed  are  insignificant. 

To  investigate  the  probable  value  of  M0 ,  Hallauer*  recalcu- 
lated a  number  of  the  tests  given  in  Tables  XII  and  XIII 
under  various  assumptions.  For  the  test  of  Sept.  8,  1875,  he 
finds  that  the  value  of  Qc,  the  exhaust  waste,  is  37.02  calories,  as 
given  in  Table  XIII,  when  calculated  on  the  assumptions  that 
the  steam  caught  in  the  cylinder  at  compression  and  the  work  of 
compression  can  both  be  neglected.  Assuming  that  the  steam 
caught  at  compression  is  dry  and  saturated,  and  allowing  for 
the  work  of  compression,  he  finds  that  Qc  =  38.52  calories. 
The  weight  of  steam  caught  at  compression  he  finds  to  be 
0.00432  kilogram  under  this  supposition.  He  then  assumes 
that  just  enough  water  is  present  in  the  cylinder  at  compres- 
sion to  give  the  same  intrinsic  energy  for  the  mixture  at  the 
beginning  and  end  of  compression,  calculated  from  the  known 
volumes  and  pressures  at  those  points.  The  weight  of  the  steam 
and  water  in  the  cylinder  during  compression  is  0.05082  kilo- 
gram on  this  supposition,  and  the  exhaust  waste  is  Qc  =  38.17 
calories.  The  differences  of  the  three  values  of  Qc  thus  deter- 
mined are  less  than  the  probable  error  of  the  experiment.  It 
should  be  noted  that  the  weight  of  steam  exhausted  from  the 
engine  per  stroke  was  0.2634  kilogram,  and  that  the  moisture 
in  this  steam  was  10.63  per  cent,  as  determined  from  the  initial 
and  final  temperatures  of  the  injection-water. 

Finally,  Hallauer  finds  that  if  it  be  admitted  that  the  weight 
of  water  and  steam  caught  in  the  cylinder  at  compression  is 
equal  to  that  exhausted  per  stroke^ — an  assumption  which 

*  Bulletin  de  la  Soc.  Ind.  de  Mulhouse,  vol.  Iv.  1881. 


336  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Zeuner  claims  to  be  reasonable,  and  which  would  require  only 
a  thin  layer  of  water  adhering  to  the  cylinder  walls, — then  he 
finds  that  the  walls  of  the  cylinder  must  have  yielded  12.22 
calories  during  compression  ;  an  amount  which  may  be  consid- 
ered absurd.  At  the  same  time  he  finds  that  this  particular 
assumption  makes  Qc  =  42.66  calories,  or  that  it  involves  a 
larger  exhaust  waste. 

If  it  be  assumed  that  the  interchange  of  heat  between  the 
steam  and  the  walls  of  the  cylinder  during  compression  is  in- 
considerable in  the  test  of  Nov.  28,  1873,  Hirn  *  finds  that  the 
equations  given  by  Zeuner  give  for  the  interchange  of  heat 
between  the  steam  and  the  walls  of  the  cylinder 


Qa  —  52.61  calories  —  68.59^  J 
Qb  =  21.07  calories  —  43. 296^  ; 
Qc  —  31.5  calories  —  25.36^ ; 


the  several  values  of  Q  being  successively  for  admission,  ex- 
pansion, and  exhaust,  and  G0  being  the  weight  of  water  and 
steam  caught  in  the  cylinder  at  compression,  which  is  assumed 
to  be  unknown  so  that  there  are  four  unknown  quantities  with 
three  equations. 

If  it  be  assumed  that  the  steam  is  dry  and  saturated  at 
compression,  then  for  this  test  G0  —  0.00112  kilogram,  and 

Qa  =  52-53  calories; 
Qb  =  21.02  calories; 
Qc  =  3 1. 47  calories. 

On  the  other  hand,  if  it  may  be  assumed  that  any  one  of 
the  three  quantities  Qa,  Qb,  or  Qc  is  inconsiderable,  and  can  be 
neglected,  then  G0  may  be  calculated  directly.  First  suppose 
that  Qb  is  zero,  or  that  there  is  no  interchange  of  heat  during 
expansion ;  then 

G0  —  0.487  kilogram  ; 

Qa  =  19.21  calories; 

Qc  =  19.18  calories. 

*  Bulletin  de  la  Soc.  Ind.  de  Mulhouse,  vol.  lii.,  1882. 


HIRN'S  ANALYSIS.  337 

Now  the  weight  of  vapor  exhausted  per  stroke  is  0.3732  kilo- 
gram, so  that  the  assumption  requires  that  the  weight  of  water 
in  the  clearance  shall  exceed  the  weight  of  steam  exhausted. 
But  while  this  condition  is  supposable,  it  is  impossible  that  the 
walls  of  the  cylinder  should  receive  heat  from  the  steam  during 
exhaust,  as  is  indicated  by  the  positive  sign. 

If  it  be  assumed  that  there  is  no  exhaust  waste,  that  is,  that 
Qc  =  o,  then 

G0  =  1.245  kilograms; 

Qa=  —  32.78  calories  ; 

Qb  =  +32. 78  calories; 

which  would  require  that  the  walls  during  admission  should 
yield  heat  to  the  entering  steam,  and  that  they  should  absorb 
heat  during  expansion. 

The  conclusion  is  inevitable,  that  there  is  an  energetic  inter- 
change of  heat  between  the  steam  and  the  walls  of  the  cylin- 
der. It  also  seems  probable  that  there  cannot  be  great  error 
in  assuming  that  the  steam  is  dry  and  saturated  at  com- 
pression. 


CHAPTER   XVIII. 

VARIOUS     STEAM-ENGINE  TESTS. 

Tests  on  Donkin  Engines. — A  large  number  of  efficiency 
tests  were  made  by  Mr.  Bryan  Donkin,  Jr.,  and  Mr.  Salter  on  an 
engine  built  for  the  purpose  by  Messrs.  B.  Donkin  &  Co.,*  in 
which  the  methods  of  making  the  tests  and  calculations  were 
similar  to  that  outlined  on  page  242. 

The  engine  was  a  two-cylinder  tandem  compound  engine ; 
each  cylinder  was  provided  with  a  steam-jacket,  which  could  be 
supplied  with  steam  in  various  ways,  and  the  water  condensed 
from  each  jacket  could  be  drawn  off  and  weighed  separately. 
Each  cylinder  had  the  steam  distributed  by  a  plain  slide-valve, 
and  the  small  cylinder  had  a  cut-off  valve  on  the  back  of  the 
main  valve. 

The  heat  brought  into  the  cylinder  of  an  engine  may  be 
divided  into  three  parts  :  one  part  is  changed  into  work,  a  sec- 
ond part  is  lost  by  radiation,  and  a  third  part  is  carried  away 
by  the  condensing  water.  In  these  experiments  the  part 
changed  into  work  was  determined  by  taking  indicator-dia- 
grams at  regular  intervals ;  the  power  of  the  engine  was  also 
measured  by  a  friction  brake.  The  heat  carried  away  by  the 
condensing  water  was  determined  by  taking  the  temperature 
of  the  injection-water  before  it  was  delivered  to  the  jet-conden- 
ser, and  the  temperature  of  the  mingled  condensing  water  and 
condensed  steam  discharged  by  the  air-pump,  and  by  gauging 
the  latter  on  a  weir  i£  inches  wide.  Allowance  was  made  for 
the  water  condensed  in  the  jackets  when  they  were  in  use.  The 
heat  lost  by  radiation  was  not  determined,  but  was  assumed  to 

*  Engineering,  vol.  xxi.  p.  203;  vol.  xl.  pp.  317  and  342;  vol.  xlii.  pp.  487 
and  577. 

338 


VARIOUS  STEAM-ENGINE    TESTS, 


339 


be  small  in  amount,  and  nearly  if  not  quite  constant.  The 
number  of  thermal  units  carried  away  by  the  condensing  water 
per  indicated  horse-power  per  minute  was  considered  to  be  the 
measure  of  the  economy  of  the  engine  ;  that  is,  it  was  considered 
that  the  most  economical  method  of  running  the  engine  was 
that  one  in  which  this  quantity  Was  smallest. 
The  dimensions  of  the  engine  were : 

Diameter,  small  cylinder, 6  in.  minus  -j^-g-  in. 

large         " 10   "        "       -^    " 

Stroke, I  foot. 

Piston  displacement :    small  cylinder,  .     .  336.4  cu.  in. 

large    '    "  .     .  939.1   "      " 

Clearance,  small  cylinder: 

crank  end  :  clearance  (-|  in.), 

passage, 
back  end  :    clearance  (^  in.), 

passage, 

Clearance,  large  cylinder: 

crank  end :  clearance,  (f-  in.), 

passage, 
back  end :    clearance, 

passage,  (£  in.), 

Small-cylinder  exhaust  passage  and 
large-cylinder  steam-chest, 


Cubic 

Per  cent  of  small 

inches. 

piston  displacement. 

17-5 

5.2 

24.3 

7.22 

17.5 

5.2 

24-3 

7.22 

Cubic 
inches. 

Per  cent  of  large 
piston  displacement. 

67.7 

7.2 

26.9 

2.86 

64.2 

6.84 

27.8 

2.96 

180.5 


19.2 


The  ratio  of  expansion  is  calculated  as  follows :  The  cubic 
contents  of  the  low-pressure  cylinder  -(-  the  cover  end-clearance 
and  passage  -f-  high-pressure  exhaust  passage  and  low-pressure 
steam-chest  +  the  high-pressure  cylinder  -f  the  front  clearance 
and  passage  =  1589.8  cubic  inches.  The  cubic  contents  of  the 
high-pressure  front  clearance  and  passage  =41.8  cubic  inches. 

Total  cubic  content  =  1589.8 
Cubic  content  before  steam  is  cut  off  =  ratio  °f  exPansion* 

The  experiments  to  determine  the  friction  of  the  engine 
were  made  with  the  steam  at  40  Ibs.  pressure  in  the  boiler. 


340  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

• 

Steam  was  passed  through  the  jacket  of  the  low-pressure  cylin- 
der before  it  reached  the  engine,  but  there  was  no  steam  in  the 
jacket  of  the  high-pressure  cylinder.  The  stop-valve  was  nearly 
closed,  and  the  governor  was  connected  to  the  throttle-valve  ; 
the  cut-off  was  at  about  one  eighth  of  the  stroke.  The  brake 
strap  was  lifted  off  the  fly-wheel,  and  when  the  revolutions 
were  steady  three  sets  of  indicator-diagrams  were  taken.  Sev- 
eral experiments  were  made,  and  a  fair  average  of  the  whole, 
with  the  speed  at  96  revolutions,  gave  the  friction  as  1.37 
horse-power. 

Table  XIX  gives  the  data  and  results  of  tests  made  (i) 
with  no  steam  in  either  jacket,  but  with  air  in  both  ;  (2)  with 


•:No.Jacketi) 


O      ®87          4ff     WJEi*^"    "Both 
*yU- — ^     ©  Jacket's 


FIG.  62. 

steam  passed  through  the  jacket  of  the  high-pressure  cylinder 
to  the  steam-chest  of  that  cylinder,  and  with  air  in  the  low- 
pressure  jacket ;  (3)  with  steam  in  the  low-pressure  jacket  only ; 
(4)  with  steam  passed  through  the  low-pressure  jacket,  thence 
through  the  high-pressure  jacket,  and  thence  to  the  high-pres- 
sure steam-chest  ;  (5)  with  the  steam  throttled  and  passed 
through  the  low-pressure  jacket  and  thence  to  the  high-pressure 
steam-chest.  The  results  of  the  first  four  series  of  tests  are 
also  represented  by  Fig.  62,  in  which  curves  are  drawn  with 


VARIOUS   STEAM-ENGINE    TESTS. 


341 


TABLE   XIX. 
TESTS  ON  DONKIN  ENGINE. 


p 

g 

si. 

Horse- 

Tempera- 
ture of  con- 

V 
V"    % 

05 

c 

•a 
c 

c 

'a 

1 

§ 

X 

"o 

power. 

densing 

IJ 

£o 

v  S. 

rt 

c  ti 

u 

U 

1 

v  jg 

<8 

water. 

V  § 

£7* 

acL 

rt  C 

Conditions 

0. 

9* 

I 

"5  g 

•g 

rt  w 

rt  5 

C/3    U 

—  -a 

of  Test. 

03 

c 

_0 

§  . 
15  v 

Cu 

I 

11 

c    . 

•o 

oS 

fe   O 

"o  <u 

ll 

il 

1 

0^2 

"o 
o 

.2  « 

'T!  C 

il 

3  <u 

§ 

« 

a 

1.S 

i! 

CT3        i 

S    C/3 

13  s 

1 

u 

1 

Q 

I8 

•3 
c 

« 

I 

rt 

Is 

Ia 

I1 

56 
53 
55 
64 

No  jackets  on. 
Boilure-pres- 
sure,  43  pds. 

98.17 
96.61 
96.18 
96.31 

1 

8.38 
7.54 
5.8 
4.45 

30 

3° 
30 
3° 

16' 
26.1 

8io4 
9-37 
10.51 

4.91 
5-79 
6-73 
7-7 

60.5 
60.37 

60.75 

103.75 

104  .  1 

102.34 

102.4 

86.25 

98 

135-5 
145 

525 
533 
619 
574 

None. 

High-pressure 

jacket  only. 

59 
57 

58 

Steam  taken 
from  jacket  to 
steam-chest  of 
high-pressure 

97-97 
97-93 
97-5 

| 

10.78 
7.73 
7.01 

3° 
30 
30 

27 
27 
27 

6.72 
8.03 
8.84 

4-89 
5-87 
6.82 

59-75 
59-25 
60 

98.42 
94.98 

95-75 

73 
94-5 
103-5 

0-475 
0.52 

0.475 

420 
420 
418 

None. 

cylinder.  Boiler- 

pressure,  43-44. 

~88 

102.27 

T% 

15.8 

30 

27-5 

6.88 

S-11 

50-75 

87-5 

80 

0.66 

427 

None. 

I    %  oz. 

91 

Low-pressure 

97-15 

T3 

10.78 

30 

27 

7.69 

5-83 

47 

94 

66.5 

1-75 

406 

-<  suet  per 
(  hour. 

28 

jacket  only. 

106.8 

% 

9.74 

3° 

27.8 

8.72 

7.48 

48.4 

85.6 

88.8 

•7 

380 

23 
35 

Boiler-pressure, 
40  to  41  pds. 

I04-5 
101  .3 

¥ 

9.14 

8.38 

30 
3° 

27.2 
27.6 

9.02 
9.82 

I'.i* 

49-75 

101.25 
92-5 

68.25 
92-5 

.62 
.64 

388 
383 

Suet. 

30 

no.  2 

£ij 

7.54 

3° 

27-5 

10.94 

8.82 

48'5 

97-3 

85-5 

.69 

385 

31 

106.4 

fl3 

7.18 

3° 

27.7 

11.44 

10.  II 

51-5 

97-23 

101.75 

•77 

407 

32 

99 

K 

5.38 

30 

27.8 

12.39 

10.89 

52 

92.6 

130.5 

.67 

427 

Steam  passed 

41 
40 

through  low- 
pressure  jacket, 

93-32 
103.4 

g 

13.1 
13.1 

30 
3° 

27.1 

26.9 

6-5 
7.01 

4.67 

52.37 
54 

92.18 
94-5 

56-75 
60.25 

0.4 
0.56 

347 
348 

None. 
Suet. 

44 
45 

thence  to  high- 
pressure  jacket, 

89.39 
99-35 

% 

8.38 
9.14 

30 

3° 

26.8 
26.7 

8.85 
9-05 

6-95 

57-37 
57-37 

101.78 

IO2.  72 

74/75 
73-25 

0.23 
0.61 

375 

367 

None. 

46 

thence  to  valve- 

99.19 

HJ 

7.54 

3° 

26.9 

9.08 

6.94 

57-25 

99 

82.5 

o-7 

372 

* 

48 
42 
49 

chest  of  high- 
pressure  jacket. 
Boiler-pressure, 

97-77 
97.6 

97-5 

1 

6.7 

5.8 
4.64 

3° 
30 
3° 

26.6 
27.2 
26.6 

10.53 
1  1  .  82 
12.87 

8.80 
9.76 
10.7 

58 
53-25 
58.12 

100.2 

89.85 

100.9 

95-75 
130.65 
123.5 

0.64 
0.61 
0.67 

385 
405 
410 

, 

41  to  45  pds. 

129 

Throttling  ex- 

97-25 

A 

8.38 

3° 

27.25 

8.65 

6.81 

62.5 

93-i 

108  .  06 

0.64 

382 

l£  oz.  suet 

131 
127 
135 
128 
132 
130 
134 

periments. 
Steam  taken 
through  low- 
pressure  jacket 
to  high-pressure 
steam-chest. 
Boiler-pressure, 
40  to  42  pds. 

96.2 
96.8 
96.9 

IO2 
100.3 
IOI  .2 
103.13 

3 

None. 

8.38 
7.73 
15.8 

30 
3° 
30 
30 
30 
30 
30 

27-5 
27-25 
27 
26.4 
26.75 
27.12 
27 

9.22 
9-25 
5-79 
6.16 
6.23 
6.06 
5-94 

6.73 
6.77 
3-88 
4.01 
4.01 
4-05 
4.12 

60.25 
62.25 

59-75 
62.37 
61  .25 
60.75 
58.0 

95-23 
96.87 
94-7 

103.  12 
102.6 

104.6 

95-03 

105-33 
102.52 
68.4 
68.56 
65-5 
61.37 
72.2 

.62 
.67 

Is 
•50 
.42 

•45 

394 
384 
413 
453 
437 
444 
450 

per  hour. 

342  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

the  indicated  horse-power  as  abscissae  and  with  the  number  of 
thermal  units  per  horse-power  per  minute,  carried  away  by  the 
condensing  water,  as  ordinates.  These  curves  show  in  a  most 
striking  manner  the  action  of  steam-jackets  on  this  engine. 

In  the  course  of  the  tests  it  was  found  that  if  an  excessive 
amount  of  melted  suet  was  fed  into  the  cylinder  it  formed  a 
non-conducting  coat  on  the  wall,  and  lessened  the  action  of  the 
walls  on  the  steam.  Two  sets  of  experiments  were  made  to 
determine  the  extent  of  this  effect :  in  the  first,  steam  was  let 
into  the  high-pressure  jacket  only,  and  suet  was  fed  into  the 
high-pressure  steam-chest  at  regular  intervals ;  in  the  second 
set  neither  jacket  was  supplied  with  steam,  and  suet  was  fed 
into  the  high-pressure  steam-chest.  The  data  and  results  of 
these  tests  are  shown  in  Table  XX,  together  with  the  data  and 
results  of  tests  made  by  feeding  water  into  the  low-pressure 
cylinder.  The  results  of  feeding  in  suet  are  also  shown  by 


X104 


mean 

of  two  x^«>Xy94  LOW    88  Pressure  Jacket 


0  1  2  3  4  5  6  7  8  9  10          11          12          13 

FiG.  63. 

Fig.  63,  in  which  the  abscissae  are  ounces  of  suet  fed  per  hour, 
and  the  ordinates  are  thermal  units  per  horse-power  per  minute 
carried  away  by  the  condensing  water. 

The  importance  of  these  experiments  on  feeding  suet  and 
on  feeding  water  into  the  cylinders  of  the  engine  is  connected 
with  the  question  as  to  the  influence  of  the  walls  of  the  cylin- 
der on  the  steam,  and  especially  with  the  question  as  to 
whether  the  initial  condensation,  re-evaporation,  and  exhaust 


VARIOUS  STEAM-ENGINE    TESTS. 

TABLE   XX. 
TESTS  ON  DONKIN   ENGINE, 


343 


Conditions  of 
the  Test. 

Revolutions  per  minute. 

Cut-off,  high-pressure 
cylinder. 

Ratio  of  expansion. 

Duration  of  the  experi- 
ment, minutes. 

Vacuum,  inches  of 
mercury. 

Horse- 
power. 

g| 

Thermal  units  per 
horse-power  per  min. 

Lubricant. 

Pounds  of  water  fed 
into  large  cylinder 
per  minute. 

Temp'ture  of  the  wateri 
fed  into  large  cylin. 

-3s 

£8, 
i—  » 

Kind  used. 

Ounces  per  hour. 

Intervals  of  feed- 
ing, minutes. 

Indicated. 

A 

rt 

- 

95 

92  1 
93  f 

90] 
911 
96| 
97  }- 
98 
99 
101 
89 
94 
88 

Suet  fed  into 
high-pressure 
steam-chest  in 
varying  quanti- 
ties at  regular 
ntervals.  Low- 
pressure  jacket 
only.     Boiler- 
pressure,  40  to 
44  pounds. 

96-93 
104.47 

96.76 

97.27 
103.46 
97-43 

JA 

r° 

(  T7B 

7-9 
7-73 

H 

10.78 
9-74 
10.78 

30 
30 

15  I 

t0( 
3°) 

15 
3° 

26.75 
26.37 

27.25 

27.25 
26.4 
27-25 

9-47 
9.70 

8.68 

7.48 
9-37 

7-45 

6.78 
7-31 

6.46 

5-84 
7-24 

5.85 

°-*S3 
0.165 

O.II2 
0-153 

o.  162 

0.215 

441 
412 

412 

406 

402 
402 

None. 
Suet. 

0.5 

0-75 

1-50 
3- 

\i 

5 

.... 

.... 

104 
102 

108 

109 

100 
103 
106 
107 

Suet  fed  into 
high-pressure 
steam-chest  in 
varying  quanti- 
ties and  at  regu- 
lar, intervals. 
Air  in  both 
jackets.    Boiler- 
pressure,  43  to 
44  pounds, 
[n  tests  106  and 
107  suet  was 
fed  through 
grease-cock,  in 
106  to  h.  p.  cy- 
linder, in  107  to 
both  cylinders. 

96.5 
96-5 

94-7 

96-53 
96.7 
96.7 
96.55 
97.6 

H 

6.4 
6.15 

6-7 
6.4 
7-36 
7-36 

20 
15 
IS 

15 

30 
15 
20 
IS 

27.25 
27-5 
27.3 

27.22 
27.28 
27-5 
27-35 
27.4 

10.79 
8.84 

9-47 
9.70 

9-31 
8.46 
8.79 
8-5 

6.75 
6-75 
6.63 

6.76 

6-77 
6.83 
6.76 
6.83 

'.'.'.'.'. 

593 
532 

500 

507 

483 
476 

449 
433 

None. 
Suet. 
(Lard 
1    oil. 
Russian 
tallow. 
Suet. 

N 

0.7 

12. 

5 

2 

I 

116 
117 
118 
121 
119 
125 
124 
128 

Water  was  run 
continually  into 
the  grease-cock 
on  low-pressure 
cylinder,  from 
which  it  was 
drawn  into  the 
cylinder  at 
varying  rates. 
In  tests  116  and 
117,  steam  was 
in  the  low-pres- 
sure jacket,  but 
in  other  tests 
was  in  neither 
jacket. 

:: 

\ 

7-54 
6.8 
5.38 
5-38 
4-5 
5-o 
4-7 

20 
15 
2O 
20 
2O 
10 
15 
15 

26.1 
25- 
27. 
25-75 
26.5 
25.2 
25-5 
25-5 

9-63 
9-23 
9.81 
8.88 
10.05 
9.04 
9-23 
8.84 

6-7 

6.79 
5-84 
6.78 
5-84 
5-8 
5-8i 

0.05 
0.09 

405 
502 
504 

559 
564 
645 
628 

Suet. 

None. 

:::: 

None. 
0-55 
None. 
0.4 

0.56 
1.4 
1.6 

150 

199 
145 
56 
203 
204 

344  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

waste  are  caused  by  the  action  of  the  metal  of  the  cylinder  or 
of  water  remaining  permanently  in  the  cylinder. 

To  further  illustrate  this  method  of  testing  engines,  the 
summary  of  results  of  two  other  tests  are  inserted.  One  test 
was  on  a  mill-engine,  and  the  other  on  an  engine  geared  to 
pumps  that  worked  at  a  slower  speed  than  the  engine. 

Both  engines  were  similar  to  the  small  experimental  engine 
already  described.  The  two  cylinders  are  placed  in  a  line  with 
each  other,  the  high-pressure  cylinder  being  situated  next  the 
crank-shaft.  The  low-pressure  cylinder  only  is  jacketed,  and 
the  steam  is  led  through  this  jacket  on  its  way  to  the  valve- 
chest  of  the  high-pressure  cylinder,  while  the  water  arising 
from  condensation  is  carried  off  by  an  efficient  steam-trap. 
The  distribution  of  the  steam  is  effected  by  ordinary  slide- 
valves,  that  of  the  high-pressure  cylinder  having  an  adjustable 
expansion-valve  at  the  back.  The  two  main  valves  are  driven 
by  a  single  eccentric,  the  spindle  for  the  low-pressure  valve 
being  a  prolongation  of  that  for  the  high-pressure  cylinder, 
while  a  second  eccentric  drives  the  expansion-valve  as  usual. 
The  steam  passages  are  all  so  arranged  that  the  cylinders  are 
completely  drained.  The  engine  is  provided  with  an  ordinary 
injection  condenser,  and  the  injection-water  is  drawn  from  an 
adjacent  river,  no  cold-water  pump  being  used. 

One  engine*  is  used  to  drive  rag  engines  at  a  large  paper- 
mill;  and  the  other f  is  geared  to  pumps  driven  at  a  slower 
speed  than  the  engine. 

Tests  on  Donkin  Mill-engine. — The  object  of  the  test 
was  to  ascertain  the  average  horse-power,  the  quantities  of  coal 
and  water  used,  and  to  account  satisfactorily  for  all  of  the  heat 
furnished  to  the  engine. 

The  feed-water  was  measured  by  two  cylindrical  cans  into  a 
cast-iron  tank  ;  the  level  of  water  in  the  tank  was  the  same  at 
the  beginning  and  end  of  the  test.  The  temperature  of  the 
feed-water  was  taken  every  twenty  minutes. 

Before  the  experiment  commenced  all  coals  were  cleared 

*  Engineering,  November  3,  1871. 

f  Proceedings  of  Civ.  Engrs.,  vol.  Ixvi. 


VARIOUS  STEAM-ENGINE    TESTS.  345 

away  from  the  front  of  the  boiler,  and  into  the  space  thus  made 
the  coal  to  be  used  on  the  trial  was  weighed.  The  coal  used 
was  Powell's  Duffryn,  and  was  of  excellent  quality. 

In  commencing  the  experiment  at  9.30  A.M.,  on  a  signal 
being  given  from  the  engine-house  the  water-level  in  the  boiler 
was  marked  on  a  scale  fixed  to  the  glass  of  the  water-gauge, 
the  pressure  of  steam  was  noted,  and  both  fires  were  at  once 
drawn,  with  the  exception  of  about  a  shovelful  left  in  each 
furnace  for  relighting.  About  12  Ibs.  of  wood  were  then 
thrown  in,  and  the  firing  commenced  with  the  weighed  coal, 
the  drawn  fires  being  cleared  away.  When  the  fires  were 
drawn  the  steam  stood  at  50  Ibs.  per  square  inch  ;  in  five  min- 
utes it  had  fallen  to  49  Ibs.  ;  but  in  fifteen  minutes  it  had  risen 
again  to  49^-  Ibs.,  and  in  twenty-five  minutes  it  was  at  54  Ibs. 
During  the  day  it  was  kept  almost  constantly  at  53  Ibs., 
scarcely  ever  varying  from  this  pressure  more  than  a  couple  of 
pounds,  and  the  mean  of  forty-nine  observations  taken  at 
intervals  of  twelve  minutes  showed  the  pressure  last  mentioned 
to  be  the  average  throughout  the  experiment. 

At  6.45  P.M.,  when  the  experiment  was  approaching  a  close, 
the  pressure  was  51 J  Ibs.,  while  at  the  end  of  the  trial  it  was 
49f  Ibs.,  or  almost  exactly  the  same  as  it  was  at  the  beginning, 
while  the  water-level  was  also  precisely  the  same.  On  notice 
being  given  from  the  engine-house  that  the  trial  was  completed, 
both  fires  were  drawn,  and  the  coal,  cinders,  etc.,  taken  out 
and  set  on  one  side  to  cool,  while  at  the  same  time  the  ash-pits 
were  cleaned  out.  When  cool,  the  materials  drawn  from  the 
fires  were  passed  over  a  sieve  with  J-inch  meshes,  and  the 
clinkers  picked  out  by  hand,  and  the  weight  was  then  found  to 
be  as  follows : 

Cinders,  siftings,  clinkers,  dirt  from  ash-pit,  2  cwt.  3  qrs. 
20  Ibs. 

The  total  amount  of  coal  charged  into  the  furnaces  during 
the  trial  was  12  cwt.,  and  the  quantity  consumed^was  thus  9 
cwt.  o  qrs.  8  Ibs.  =  1016  Ibs.  plus  its  proper  proportion  of  the 
dirt.  Of  the  siftings,  one  half  was  judged  to  be  good  fuel  and 
the  other  half  dirt,  and  the  total  quantity  of  dirt  was  thus  13 


346  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Ibs.  siftings  -f-  10  Ibs.  clinkers  +53  Ibs.  from  ash-pit  =  76  Ibs.  in 
all,  or  almost  exactly  5.66  per  cent.  Of  this  76  Ibs.  of  dirt,  12 
Ibs.  (a  quantity  rather  below  the  proper  percentage)  was  taken 
as  belonging  to  the  239  Ibs.  of  cinders  drawn  from  the  fire,  and 
the  remainder,  64  Ibs.,  was  added  to  the  fuel  actually  con- 
sumed, thus  raising  the  latter  to  1080  Ibs. 

The  quantity  of  water  fed  into  the  boiler  during  the  trial 
was  11,691  Ibs.,  and  the  evaporation  therefore  took  place  at 
the  rate  of  VoW  —  10.82  Ibs.  of  water  per  pound  of  coal. 

The  observations  made  in  the  engine-house  were  as  follows: 
I.  Every  half-hour  indicator-diagrams  were  taken  simultane- 
ously from  both  ends  of  both  cylinders  by  means  of  four  Rich- 
ards indicators  ;  2.  Half-hourly  readings  were  taken  of  the  in- 
dications of  the  steam  and  vacuum  gauges,  and  of  the  counter 
with  which  the  engine  was  provided  ;  3.  An  account  was  kept 
of  the  temperature  and  quantity  of  water  drawn  from  the 
steam-jacket  ;  and  4.  Observations  were  taken  every  quarter 
of  an  hour  of  the  quantity  and  temperature  of  the  water  pass- 
ing off  from  the  condenser.  The  water  discharged  by  the  air- 
pump  was  led  along  a  short  iron  trough  fitted  with  partitions 
which  extended  nearly  across  it.  The  water  on  its  way  down 
the  trough  was  caused  to  pass  under  and  over  and  around  the 
ends  of  these  partitions,  and  it  was  thus  thoroughly  mingled, 
and  the  temperature  rendered  uniform  throughout.  After 
escaping  the  partitions  it  was  discharged  over  a  tumbling  bay 
having  a  notch  6  in.  wide  carefully  cut  in  a  brass  plate,  while 
the  head  or  height  of  water  over  the  notch  was  taken  by  means 
of  a  hook  gauge.  The  temperature  was  taken  by  a  delicate 
thermometer,  on  which  the  water  fell  in  the  tumbling  bay. 
The  temperature  of  the  water  used  for  injection  was  also  noted 
at  frequent  intervals  during  the  day,  and  thus  the  rise  of  tem- 
perature in  passing  through  the  condenser  could  be  ascertained. 

TEST  OF  DONKIN  COMPOUND  MILL-ENGINE. 

Duration  of  trial:  from  9.30  A.M.  to  7.30  P.M., =  10  hours. 

Mean  pressure  of  steam  in  boiler-house, 53  Ibs. 

Mean  vacuum 27^-  in. 

Mean  speed  of  engine  in  revolutions  per  minute,   .    ,,-.,,.     .  46  51 


VARIOUS  STEAM-ENGINE    TESTS.  347 

Indicated  horse-power — mean  results  of  84  diagrams: 

Mean  indicated  power  developed  in  high-pressure  cylinder,     32.03  I.  H.  P. 
Mean  indicated  power  developed  in  low-pressure  cylinder,     24.85 

Mean  total  indicated  horse-power, 56.88 

Observations  of  water  from  condenser: 
Temperatures: 

Mean  initial  temperature  of  injection-water, 51°. 66 

Temperature  of  water  discharged  from  condenser,  .     .     .     83°. 32 

Rise  of  temperature  in  condenser, 31.66 

Quantities: 

Mean  head  over  tumbling  bay  6  in.  wide,  taken  by  a  hook- 
gauge, 2^-  in.  bare. 

Mean  discharge  per  minute, 606.5  Ibs. 

Pound-degrees: 

Pound-degrees   of  heat   discharged  from  condenser  per 

minute  =  606.5  X  31.66,  .     .     ;     .' 19,202 

Pound  -  degrees   per   indicated   horse-power   per    minute 

10,202 
—  -zi —  317.6 

56.88 

Water  from  trap  of  steam-jacket: 

Total  quantity  discharged  during  ten  hours, 1,020  Ibs. 

Quantity  discharged  per  hour, 102  " 

Feed-water: 

Initial  temperature, 6i°.75 

Quantity  evaporated  during  ten  hours  =  108  cans,  weigh- 
ing each  io8£  pounds  =        11,691  Ibs. 

Quantity  evaporated  per  hour, 1,169.1" 

Quantity   evaporated  per  indicated  horse-power  per  hour,  20.55      " 

Quantity  evaporated  per  pound  of  coal  consumed,  ....  10.82      " 

Coal:  Description — Powell's  Duffryn: 

Quantity  consumed  during  ten  hours, 1,080  Ibs. 

Quantity  consumed  per  square  foot  of  fire-grate  per  hour,  3.27      " 

Quantity  consumed  per  indicated  horse-power  per  hour,       .  1.9        " 

Test  on  Donkin  Pumping-engine. — In  the  tests  on  this 
engine,  in  addition  to  the  determination  of  the  efficiency,  it 
was  desired  to  distinguish  between  the  efficiency  of  the  boiler, 
that  of  the  engine,  and  that  of  the  pumps.  The  method  of 
making  the  tests  was  similar  to  that  already  described  for  the 
mill  engine.  In  this  test  also  the  feed-water  was  measured  in 
cans,  and  the  condensed  water  from  the  jacket  on  the  low- 
pressure  cylinder,  through  which  the  steam  passed  on  the  way 


348  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

from  the  high-  to  the  low-pressure  cylinder,  was  also  measured 
in  cans. 

The  engine  drove,  through  gearing,  two  sets  of  pumps,  one 
of  which  lifted  water  from  a  well  into  a  tank,  and  the  other 
forced  water  from  this  tank  into  the  delivery  main.  The  in- 
jection-water was  taken  from  this  tank,  and  consequently  the 
force-pumps  delivered  so  much  less  water  than  the  lifting- 
pumps. 

On  the  2Qth  of  March  a  separate  test  was  made  to  deter- 
mine the  power  required  to  drive,  respectively,  the  engine  and 
gearing  only,  and  the  engine,  gearing,  and  lifting  pumps.  The 
distribution  of  power  was  found  to  be — 

Engine  and  gearing, 12.15  horse-power. 

Lifting  pumps,  .  ...    ..*-.»     .     39.3 1  " 

Forcing  pumps, 35-57          " 


Total, 87.03  " 

The  test  was  continuous,  but  the  calculation  has  been  made 
for  the  first  five  hours  and  the  second  five  hours,  as  well  as  for 
the  entire  run  of  ten  hours. 

TABLE  XXI, 

TEST  ON  DONKIN  PUMPING  ENGINE. 

April  5,  1881. 

The  experiments  were  made  by  Messrs.  B.  Donkin,  Jr.,  Martin,  Salter,  and 
Bacon. 

ENGINE. 

Class  of  engine — compound,  condensing,  horizontal  (low-pressure  cylinder 
jacketed). 

Name  of  maker — Bryan  Donkin  &  Co. 

Diameters  of  cylinders  i6l|  inches  and  30  inches:  diameter  of  piston-rods 
2f  inches  and  4  inches  (all  from  gauges). 

Length  of  strokes,  3  feet. 

Lubricant  used  in  cylinders — Engelbert's. 

Cylinder  lubricated  every  hour:  quantity,  about  7  ounces  per  hour. 

BOILER. 

Class  of  boiler — Lancashire. 
New  in  1872. 


VARIOUS  STEAM-ENGINE    TESTS. 


349 


Chief  dimensions  25  feet  long  by  6  feet  diameter.  Two  flues,  each  2  feet 
2  inches  in  diameter. 

Total  heating  surface,  612  square  feet.  Boiler  and  flues  clean  inside  and 
out. 

Grate  surface — two  grates  each  2  feet  2  inches  by  6  feet,  together  26  square 
feet. 

Blow-off  cock  tight.  Fire  doors  opened  only  for  firing.  Direction  of  smoke 
— through  tubes,  under,  split  along  sides  to  chimney. 

Fires  8  inches  thick,  stoked  ten  times  each  furnace,  or  every  hour. 

Pounds  of  coal  per  hour  per  square  foot  of  heating  surface,  0.287. 

Pounds  of  water  per  hour  per  square  foot  of  heating  surface,  2.720. 

Temperature  of  engine-house,  62^°  ;  temperature  of  outer  air,  40°. 


Ten 
hours. 

First 
ive  hours. 

Second 
five 
hours. 

Pressure  of  steam  in  boiler-house  

.  .Ibs. 

52 
10 

27i 

55-25 
33,148 

46.36 
40.67 

52± 

27i 

57-35 
17,205 

48.55 
42.66 

5  if 
5 

27i 

53.14 
15,943 

44.17 

38.68 

Duration  of  trial,  from  9  A.M.  to  7  P.M  without 

stop- 
.hrs. 

Revolutions  per  minute               ...          ....... 

INDICATED  H.  P. 
Indicated  power  high-pressure  cylinder     .    .  . 

Indicated  power  low-pressure  cylinder  

Total  Indicated  H.  P  

87.03 

91.21 

82.85 

WATER  FROM  CONDENSER. 

54.25 
85.  -06 

54.25 
86.27 

54-25 

83-85 

Temperature  of  water  discharged  from  air-pump   " 

30.81 

32.02 

29.60 

Mean  discharge  per  minute  

.  .Ibs. 

857 
303 

1,365 

i#i 

1.56 

85 
16,731 
1,673 
19.22 

9-52 

865 
303 

710 
142 

84.9 
8,802 
1,760 
19.30 

849 
303 

655 
131 

85.1 

7,929 
1,586 
19.14 

Thermal  units  per  Indicated  H.  P.  per  minute 

WATER  FROM  STEAM-JACKET. 
Total  quantity  discharged  during  ten  hours..  . 
Quantity  discharged  per  hour  

.  .Ibs. 

"         per  Indicated  H.  P.  per  hour..  

« 

FEED-WATER. 

Quantity  evaporated  during  ten  hours  

..Ibs 

euantity  evaporated  per  hour 

uantity  evaporated  per  I.  H.  P.  per  hour  " 
Quantity  evaporated  per  Ib.  of  coal  consumed, 
from  85°  .     " 

35O  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  feed-water  was   measured  in  a  can  holding  exactly  100  Ibs.  (special 
standard)  at  80°. 

COAL. 

Fires  drawn  at  beginning  and  end,  and  28  Ibs.  of  wood  used  for  lighting  up, 
14  Ibs.  each  fire. 

1,792  Ibs.  put  on  fires,  less  35  Ibs.  (=  half  of  large  cinders  drawn  from 
fires)  = 

Lbs. 

Quantity  used  during  ten  hours, i>757 

"     per  square  foot  of  fire-grate  per  hour,    .  6f 

"  "     per  indicated  H.  P.  per  hour 2.02 


Weight  of  dirt  and  refuse  not  burnt  94^  Ibs.  small  cin-  i  i  —  ai 

ders  +  35  Ibs.  large  cinders  -f  16  Ibs.  clinkers  =  \ 

Length  of  steam-pipe,  55  feet,  all  covered.     Steam-pipes  all  tight. 
All  feed-pipes  visible  and  tight. 


RESULTS  AND  EFFICIENCY  OF  THE  WATER-PUMPS,  AND  COM- 
PARISON OF  THE  CONTENTS  OF  THE  PUMPS  WITH  THE 
WATER  PUMPED. 

THREE  DEEP-WELL  OR  LOWER  PUMPS. 

Dimensions  and  calculated  contents: 

Pumps  14  inches  diameter,  mean  stroke  2  feet  8f  inches. 

Contents  of  these  three  pumps  8.755  cubic  feet  =  546.3  Ibs.  per  revolution. 

Mean  speed  for  ten  hours  =  12.174  revolutions  per  minute. 

Contents  per  minute  =  6,651  Ibs. 
Quantity  actually  pumped: 

Mean  height  over  2  feet  3  inches  bay  in  engine-house  =  4-395  inches. 

Temperature  of  water  54°. 

Quantity  =  6,183  IDS-  Per  minute. 
Efficiency: 

6,183  •*-  6,651  =  93  per  cent  water  lifted  of  theoretical  contents. 

THREE  FORCE  OR  UPPER  PUMPS. 

Dimensions  and  calculated  contents: 

Pumps,  12  inches  diameter.     Strokes,  two  2  feet  if  inch,  one  2  feet  2  inches. 

Contents  of  these  three  pumps  5.09  cubic  feet  =  317.6  Ibs.  per  revolution. 

Mean  speed  for  ten  hours  =  20.819  revolutions  per  minute. 

Contents  per  minute  =  6,612  Ibs. 
Quantity  actually  pumped: 

Same  as  lower  pumps  (6,183  Ibs.)  less  831  Ibs.  used  for  injection  =  5,352  Ibs. 
Efficiency: 

5,352  -*-  6,612  =  81  per  cent  water  lifted  of  theoretical  contents. 


VARIOUS  STEAM-ENGINE    TESTS. 


351 


Comparison  of  measurement^)  Inches.  Lbs. 

of   water   in  engine-house  |  Engine-house,  4.38  height    =  6,155 

3.38      "      ) 
3-27      "      \~ 

two  i  foot  6  inches  bays.  |  Add  injection  (water)  831 

For  about  eight  hours.         J  Leak  of  rising  main  (measured)     10    6,262 


over  2  feet  3  inches  bay,  I  Reservoir, 
with  that  at  reservoir  over  i 


,421 


The  latter 
former. 


per  cent  more  nominally  than  the 


Percentage  of  foot-pounds  of  \  Lbs.     Feet.  H.  P.     Foot-lbs. 

water  lifted,  of  foot-pounds  >•  Lower  pumps,  6,183    198  lift  =  37.1    (of  33,000) 
of  steam-pistons.  )  Upper       "        5,352    148    "   =24.1    61.2  H.  P. 

Steam-pistons,  87.03  " 

Foot-pounds  of  water  lifted,   per  cent  of  foot- 

pounds steam-pistons,  70. 
Average  velocity  of  water  in  rising  main,  1.3  foot  per  second. 

HEAT  ACCOUNT  OF  THE  STEAM-ENGINE    IN   THERMAL  UNITS 
OR   POUND-DEGREES    PER   MINUTE. 


Units. 


Per  cent. 


Dr.  to  boiler: 

Feed,  27.888  Ibs.  X  (1,204°. 8  —  85°  =)  1,119°. 8  = 


By  power,  87.03  I.  H.  P.  X  42.76  = 

By  waste  water  from  condenser: 

Injection,  831.33  Ibs.  X  (85°. 06  —  54°. 25  =)3o°.8i  =  25,613 

Condensed^)  _,  , 

Feed,  27.89  Ibs.  —  water  from  trap 

2.30  Ibs.  =  25.59  lbs-  X  (85°. 06  \-=.  2 

-  85°  =)  .06°  = 


3^.229 


3,721 


=  11.9 


steam 
in  waste 
water. 


By  water  from  steam-trap  2.30  lbs.  X  (212°  —  85°  =)i27°  = 
By  balance  unaccounted  for,  radiation,  etc.  =  .     .     .     . 


25,615 

293 

i,  600 


82.4 
0.9 
4.8 


31.229 


Major  English's  Tests. — In  November  and  December, 
1886,  tests  were  made  by  Major  Thomas  English,  R.  E.,*  to 
ascertain  the  most  economical  method  of  working  some  direct- 
acting,  high-pressure,  fly-wheel  pumping-engines,  intended  for 


*  Proceedings  of  the  Inst.  M.  E.  1887. 


352  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

use  in  a  hot  climate,  where  fuel  was  dear,  water  scarce,  and 
where  difficulties  of  transportation  prohibited  heavy  weights. 
The  first  object  of  the  tests  was  to  determine  whether,  under 
the  circumstances,  it  was  advisable  or  not  to  use  a  surface  con- 
denser. The  results  of  the  tests  shown  in  Table  XXII  show 
that  the  economy  of  the  engine  was  small  and  the  consumption 
of  steam  was  not  satisfactory  whether  the  engine  was  run  con- 
densing or  non-condensing.  In  addition  to  ascertaining  the  steam 
consumption,  Major  English  made  a  very  complete  analysis  of 
the  distribution  of  the  heat,  as  is  shown  by  the  table,  and  for 
this  reason  the  tests  are  of  interest.  Each  engine  consisted  of 
a  pair  of  horizontal  cylinders,  16  inches  diameter  by  18  inches 
stroke,  lagged,  but  not  jacketed.  Each  cylinder  drives  a  differ- 
ential pump  on  the  prolongation  of  the  piston-rod,  with  rams  4 
inches  and  5f  inches  diameter,  working  up  to  700  pounds  on 
the  square  inch.  The  piston-rods,  2\  inches  diameter,  pass 
through  both  ends  of  the  steam-cylinder,  and  are  connected  by 
a  crank-shaft,  which  has  cranks  at  right  angles  and  a  fly-wheel 
on  each  end.  The  engines  are  sufficiently  self-contained  to 
wotk  on  a  foundation  of  three  timbers  bolted  together  with  dis- 
tance blocks.  Each  cylinder  has  a  main  or  distribution  slide- 
valve,  and  on  its  back  cut-off  plates  that  can  be  adjusted  by 
hand  to  give  different  rates  of  expansion. 

The  steam  during  the  tests  was  furnished  by  three  multi- 
tubular  boilers  of  the  locomotive  type.  Two  of  these  boilers 
were  used  together  to  furnish  steam  for  one  main  engine,  an 
air-pump  engine  and  a  feed-pump.  The  surface  of  the  steam- 
pipe  leading  from  the  boilers  to  the  engine  was  141  square 
feet.  During  some  of  the  tests  this  steam-pipe  was  jacketed 
with  steam  from  a  separate  boiler  at  140  pounds  pressure. 

The  air-pump  and  circulating-pump  were  operated  by  one 
auxiliary  engine  with  a  steam-cylinder  10  inches  in  diameter  by 
14  inches  stroke.  The  feed-pump  was  a  direct-acting  Worth- 
ington  pump.  The  steam  from  these  two  auxiliary  engines 
was  condensed  in  a  surface  condenser,  collected,  and  weighed. 
The  exhaust  from  the  main  engine  was  in  all  the  tests  con- 
densed in  a  tubular  surface  condenser,  collected,  and  measured 


VARIOUS  STEAM-ENGINE    TESTS.  353 

In  a  tank  of  known  capacity.  During  the  non-condensing  tests 
the  air-pump  was  disconnected  and  the  exhaust  was  condensed 
at  atmospheric  pressure. 

The  average  evaporation  during  the  tests  was  7.9  pounds  of 
water  per  pound  of  coal  ;  the  rate  of  combustion  varied  from 
6.5  to  12.4  pounds  per  square  foot  of  grate  surface  per  hour. 
No  priming  worth  notice  appeared  at  any  time. 

The  indicator-diagrams  were  taken  by  a  Richards  indicator 
with  a  30  spring.  The  spring  was  tested  by  the  makers  after 
the  tests,  and  was  stated  to  be  correct.  The  clearance  of  the 
engine  is  seven  per  cent  of  the  piston  displacement. 

The  data  and  results  of  the  tests  are  given  in  Table  XXII, 
which  requires  little  explanation  in  addition  to  that  given  by 
the  headings. 

In  columns  n,  12,  and  13  are  given  the  heat  equivalents  of 
the  total  work  without  allowing  for  back  pressure,  the  effective 
work,  and  the  work  of  the  back  pressure,  for  each  pound  of 
steam  supplied. 

The  distribution  of  the  heat  lost  at  the  end  of  the  stroke  is 
shown  by  columns  14,  15,  and  16,  calculated  from  the  condi- 
tion of  the  steam  at  release,  for  each  pound  of  steam  supplied. 
The  heat  in  the  steam  and  the  water  at  release  is  unavoidably 
rejected,  but  that  abstracted  by  the  walls  of  the  cylinder 
corresponds  to  the  exhaust-waste  Qc  of  Hirn's  analysis. 

The  thermal  unit  per  pound  of  steam,  column  17,  is  the 
difference  between  the  total  heat  of  one  pound  of  steam  at  the 
initial  pressure  and  of  the  heat  of  the  liquid  at  the  mean  back 
pressuref. 

The  condensation  at  the  end  of  the  stroke  is  the  ratio  of  the 
weight  of  dry  saturated  steam  required  to  fill  the  cylinder  up 
to  release,  to  the  actual  weight  of  steam  and  water  then  pres- 
ent in  the  cylinder. 

Column  19  gives  the  number  of  thermal  units  that  could  be 
converted  into  work  for  each  pound  of  steam  in  a  perfect  en- 
gine ;  obtained  by  multiplying  the  heat  supplied  (column  17), 
by  the  efficiency  of  a  perfect  engine  working  between  the 


354 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


TABLE 
MAJOR  ENGLISH'S  TESTS  OF  A 


Absolute  pressures. 

Consumption 
of  water. 

Number  of  Test. 

Conditions  of 
Test. 

I  cut-off. 

I 

"o 

ions  per 
e. 

L 

~~i  rt 

Mean  forward, 
Ibs.  per  square 
inch. 

Mean  back.  Ibs. 
per  sq.  inch. 

Indicated  horse- 
power. 

Lbs.  per  indi- 
cated horse- 
power per  hour 

Lbs.  per  stroke. 

Nomina 

Number 
sions. 

Revolut 
minut 

IP 

11 
csr 

.§«« 

jus 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

1 
2 
3 
4 
5 

bib 

c 

c 

0) 

•o 

Steam- 
pipe, 
jacketed. 

i 

B 

5-8 
6-7 

40.2 
39-5 
39-7 
40.4 
40.9 

71-3 
89.0 
82.6 
83-3 
87-4 

22.8 
18.9 
17.6 

19-3 
I7.0 

39-4 
36.1 
38.0 
35-0 

2.9 

3-2 
3-2 

4.2 
2.7 

57-8 
50.3 
46.6 
49-4 
46-9 

34-2 
34-0 
36-1 
38.2 
34-6 

0.205 
0.182 
o.  176 

0.194. 

0.165 

6 

7 
8 

§ 
U 

M 

! 

5-'  8 

42.2 

4°-3 
40.4 

72.6 
86.5 

23-5 
l8.7 
17.7 

44-1 
38.0 
36.1 

2.6 

2.5 

3-3 

62.0 
51-0 
47-2 

35-4 
34-7 
38.9 

0.217 
0.183 
0.190 

9 

•fs 

6-7 

41.2 

86.8 

16.0 

33-5 

2.4 

45-7 

38.8 

0.179 

10 

• 

.    jp 

j 

3-4 

40.4 

83-7 

28.8 

51-8 

J5-4 

52.4 

39-6 

0.214. 

11 

c 

^ 

5-8 

40.1 

90.9 

22.3 

41.7 

16.5 

36-2 

41.2 

o.  155 

12 
13 

If 

|tf 

A 

40.1 
39-3 

88.1 
87.8 

20.0 
20.2 

36.8 
36.6 

16.2 
15-5 

29.6 
29.6 

42-9 

51-0 

0.132 

14 

i    "~ 

c 

S  -«  '    ' 

i 

3-4 

19-8 

87.6 

28.1 

52.6 

16.6 

51-0 

41.1 

0.220 

15 

& 

rt  o,O~5  *S 

i 

5-8 

40.3 

91  .6 

21.9 

41.8 

16.7 

36.0 

42.6 

0.158 

16 

5S'C^S 

& 

6-7 

39-5 

89-3 

20.0 

36.7 

15-6 

29.7 

50.5 

0.158 

initial  temperature  and  the  temperature  due  to  the  back 
pressure. 

The  absolute  efficiency,  column  20,  is  the  ratio  of  the  heat 
changed  into  work  to  the  heat  supplied;  column  12  and  col- 
umn 17. 

The  ratio  of  the  efficiencies  of  the  actual  engine  and  of  a 
perfect  engine  (column  21)  is  the  ratio  of  the  heat  -changed 
into  work  in  the  actual  engine  (column  12),  and  the  heat 
changed  into  work  by  a  perfect  engine  (column  19). 

Major  English  gives  also  diagrams  representing  the  distri- 
bution of  heat  for  each  of  the  tests  stated  in  the  table.  The 
diagrams  are  reproduced  in  Figs.  64  and  65,  for  the  6th  and 
I4th  tests. 

The  upper  part  of  the  figure  gives  the  maximum  and 
minimum  diagram  taken  during  the  test,  with  a  few  inter- 
mediate diagrams.  The  axes  are  obtained  by  laying  off  the 


VARIOUS  STEAM-ENGINE    TESTS. 


355 


XXII. 

STATIONARY  STEAM-ENGINE. 


Total  work,  thermal 
units  per  Ib.  of  steam 
supplied. 

Effective  work,  ther- 
mal units  per  Ib.  of 
steam  supplied. 

Back-pressure  work, 
thermal  units  per  Ib. 
of  steam  supplied. 

Thermal  units  of 
heat  lost  at  end  of 
stroke. 

Thermal  units  of  heat 
supplied. 

Condensation  at  end 
of  stroke,  per  cent. 

Total  work  of  perfect 
engine,  thermal  units 
per  Ib.  of  steam  sup- 
plied. 

Absolute  efficiency  of 
actual  engine. 

Relative  efficiency  of 
actual  engine  in  per- 
centage of  efficiency 
of  perfect  engine. 

Exhaust 
steam. 

Water  in 
cylinder. 

Abstracted 
by  cylin- 
der. 

11 

80 
82 
78 
75 
80 

12 

75 
75 
7i 
66 
74 

13 

5 
7 
7 

I 

14 

59° 
543 
526 
521 
55° 

15 

38 
36 
35 
32 
35 

16 

359 
407 
427 
427 
407 

17 

1067 
1068 
1066 

i°55 
1072 

18 

39-3 
43-7 
45-5 
45-5 
43-3 

19 

244 
240 

233 
217 
249 

20 

7.0 

7-° 
6.7 

6-3 
6.8 

21 

30.8 
3i-3 
30-5 
3°-5 
29-3 

77 
79 
72 
7i 

72 

ll 

65 

5 
7 
7 

5 

567 
544 
489 
482 

43 
40 
37 
42 

384 
412 
467 
482 

1071 
1075 
1065 
1077 

41.9 
44.1 
49.2 

5°-5 

237 
252 
233 
254 

6-7 
6.6 
6.1 
6.1 

3°-3 
28.2 
28.0 
25.6 

92 
103 
107 
87 

<J\  O\O\O\ 

M  M  W  Ol 

27 
40 
46 
36 

613 
650 
684 
571 

TI 

5 
3 
5 

279 
235 
199 
332 

995 
993 
993 

995 

31-8 
27.2 
23-3 
36.1 

129 

131 
129 
131 

6-5 
64 
6.1 
5-i 

49.6 
48.1 
47-2 
39-o 

9i 

IOO 

88 

62 

61 
Si 

29 
39 
37 

g« 

621 

573 

10 

4 
5 

310 
269 
33° 

992 
994 
996 

35-i 
3°-4 
35-9 

127 

*3I 

134 

6.2 

6.1 
5-i 

48.8 
45-8 
38.1 

vacuum  line  at  the  proper  distance  below  the  atmospheric 
line,  and  by  laying  off  the  line  of  zero  volume,  allowing 
for  clearance.  The  entire  volume,  including  clearance,  is 
divided  into  ten  equal  parts,  and  ordinates  are  drawn  upon 
which  the  absolute  pressures  are  measured  to  points  shown 
by  dots  on  the  ordinates.  In  the  lower  part  of  the  figure 
the  total  height  represents  the  total  thermal  units  supplied, 
column  17,  Table  XXII.  The  curve  EE  represents  the  ther- 
mal units  per  pound  of  steam,  changed  into  work,  obtained 
from  the  area  of  the  indicated  diagram  to  the  left  of  the 
ordinate  in  question.  The  line  TT  is  obtained  by  adding  to 
the  heat  changed  into  effective  work  the  heat  per  pound  of 
steam  required  to  do  the  work  of  the  back  pressure,  which  is 
obtained  from  the  area  below  the  back-pressure  line  and  to  the 
left  of  the  ordinate.  The  line  TT,  therefore,  represents-  at 
each  ordinate  the  heat  per  pound  of  steam  required  to  do  the 


356 


THERMODYNAMICS  OF  THE   STEAM-ENGINE. 


absolute  work  up  to  that  point  of  the  stroke  of  the  engine. 
To  obtain  the  line  55,  the  fraction  x,  of  a  pound  of  the  mixture 
in  the  cylinder  which  was  steam,  was  calculated  for  each  ordi- 
nate,  from  the  volume  and  pressure,  and  the  heat  in  that  steam 
was  calculated  by  the  expression 

x(r  -f  q  —  q^ 

in  which  r  and  q  are  the  heat  of  vaporization  and  the  heat  of 
the  liquid  corresponding  to  the  pressure  measured  on  the  ordi- 


0  Volume  of  Cylinder  1  including  clearance  2  - 


0  Volume  of  Cylinder  1 'Including  clearance 


lu       20       30       40       50  .   60       70       8u        90      100 
Percentage  of  stroke  including  clearance 

FIG.  64. 


10       20       30      40      ,50       60       70       80       90 

Percentage  of  stroke  including  clearance 

FIG.  65. 


nate,  and  qQ  is  the  heat  of  the  liquid  corresponding  to  the  back 
pressure.  The  number  of  thermal  units  was  then  plotted  on  each 
ordinate  from  the  line  TT,  so  that  the  line  55  represents  the 
heat  per  pound  of  steam,  changed  into  work,  plus  the  heat  re- 
maining in  the  steam.  A  similar  calculation  was  made  for  the 


VARIOUS  STEAM-ENGINE    TESTS.  357 

fraction  of  a  pound  of  the  mixture  at  each  ordinate  that  was 
water,  using  the  expression 


and  the  line  WWwas  plotted  by  laying  off  the  quantities  thus 
found  from  the  line  55  ;  so  that  the  line  WW  represents  the 
heat  per  pound  of  steam,  changed  into  work,  plus  the  heat 
remaining  in  the  water  and  steam.  The  portion  of  the  total 
heat  received  per  pound  of  steam,  above  the  line  WW,  repre- 
sents the  heat  absorbed  by  the  walls  of  the  cylinder  ;  this 
quantity  diminishes  as  the  expansion  proceeds  on  account  of 
the  re-evaporation. 

The  dotted  curve  PP  represents  the  heat  theoretically 
necessary  to  do  the  total  work  shown  by  the  curve  TT. 

A  comparison  of  all  the  observed  results  is  shown  by  Fig. 
ooo,  in  which  the  abscissae  represent  square  feet  of  surface 
exposed  to  the  steam  throughout  the  stroke  by  the  steam- 
passages,  cylinder,  and  piston  ;  the  clearance  surface  measures 
5.24  square  feet  at  the  commencement,  and  the  total  surface 
11.98  square  feet  at  the  end  of  the  stroke.  Ordinates  measured 
downwards  from  the  top  of  the  diagram  represent  the  number 
of  thermal  units  abstracted  from  the  enclosed  steam  at  any 
point  ;  and  the  curves  are  plotted  from  such  ordinates  for  each 
point  of  the  stroke.  The  palpable  convergence  of  all  of  these 
curves  to  the  zero  of  exposed  surface  at  about  150  thermal 
units  agrees  closely  with  the  hypothesis  that  there  is  a  sudden 
initial  condensation  of  steam,  equivalent,  in  all  the  tests  on  this 
engine,  to  the  transference  of  150  thermal  units,  or  28.6  thermal 
units  per  square  foot  of  exposed  clearance  surface,  to  the  metal 
surface  of  steam-passages,  cylinder,  and  piston  ;  and  that  this 
heat  is  gradually  given  back  again  to  the  steam  during  the 
stroke,  by  re-evaporation.  The  heat  thus  regained  increases 
approximately  in  proportion  to  the  surface  exposed  ;  but 
still  leaves  in  the  metal,  at  the  end  of  the  stroke  in  this  engine, 
an  amount  of  heat  equivalent  to  0.4  thermal  unit  for  each  de- 


358 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


gree  of  difference  between  the  temperatures  corresponding  to 
the  initial  and  back  pressures. 

By  the  aid  of  this  hypothesis  the  heat  abstracted  by  the 
walls  of  the  cylinder  at  each  point  of  the  stroke  of  the  piston 
has  been  calculated,  and  is  represented  by  the  line  AA  on  the 
Figs.  64  and  65.  By  the  same  hypothesis  the  diagrams  rep- 


Initial  Condensation  and  Re-evaporation 
'Percentage  of  Stroke  0   10  20  30  40  50  60  70  80  90  100, 


iiigsiss  s§§g§§s«= 

Observed  numbers  of  Thermal  Units  abstracted  from  Steam  by  Cylinder  and  piston 

/ 

Xx 

x 

/ 

/ 

/ 

j 

/ 

/ 

/ 

< 

V 

/ 

X 

/ 

J 

^ 

/ 

(  .,  

/ 

// 

y 

A 

/ 

^^ 

Noncondensing  

I 

/ 

y$jj[& 

// 

A 

$\\/s 

•'' 

tfi 

g$ 

;-. 

':¥ 

\ 

(  Clearance-Surface  ) 
;•  including  cylinder-end  >* 
(  and  piston-face  ) 

Si 

rfj 

J 

of 

sid 

es  ' 

>£< 

yi 

ud 

jr> 

1        2        3        4        5        6        7        8        9        10      11      1  -98 
Square  feet  of  Surface  exposed  to  Steam 

FIG.  66. 


resented  by  the  dotted  lines  in  the  upper  part  of  Figs.  64  and 
65  have  been  deduced  by  the  reversal  of  the  processes  used 
in  laying  out  the  lines  EE  to  WW.  The  following  table  ex- 
hibits the  correspondence  between  actual  observed  quantities, 
and  quantities  calculated  on  this  hypothesis. 


VARIOUS  STEAM-ENGINE    TESTS. 


359 


Experiment  6. 

Experiment  14. 

Observed. 

Calculated. 

Observed. 

Calculated. 

62.0 
0.217 
6-7 

65.6 
0.2II 

7-8 

51-0 
0.220 
6.2 

57-1 
0.209 
7-6 

Major  English  draws  the  following  conclusions  from  the 
tests : 

In  order  to  obtain  the  best  results  for  any  given  range  of 
temperature  there  should  be  a  definite  relation  between  the 
surface  of  the  steam-passages,  the  diameter  of  the  cylinder  and 
the  length  of  the  stroke ;  and  that  in  the  design  of  an  engine 
the  adjustment  of  these  proportions  may  be  the  most  impor- 
tant item  affecting  economy.  The  following  table  shows  for 
two  different  points  of  cut-off  the  calculated  results  of  varying 
the  length  of  the  stroke  of  the  engine  experimented  on,  while 
the  diameter  of  the  cylinder,  the  absolute  clearance  volume 
and  the  clearance  surface  exposed,  remain  unaltered  ;  and  it 
will  be  seen  that  the  same  number  of  expansions  may  give 
widely  different  results  as  regards  the  ratio  of  efficiency  and 
the  water  consumed  per  indicated  horse-power  per  hour ;  and 
also  that,  with  the  same  length  of  stroke,  these  results  are  but 
slightly  affected  by  doubling  the  number  of  expansions. 

CALCULATED  EFFICIENCY  AND  CONSUMPTION  OF  STEAM  WITH  VARYING 
LENGTH  OF  STROKE. 


Diameter  of  cylinder,  16  inches. 
Clearance,  0.143  cubic  feet. 
Clearance  surface,  5.24  square  feet. 

Cut-off,  1.4  inch. 
Absolute         initial 
pressure,  87.4  pds. 
Bac  k  pressure  ,   2.7 
pounds. 

Cut-off,  4.25  inches. 
Absolute   initial    pressure,   71.3 
pounds. 
Back  pressure,  2.9  pounds. 

Length  of  stroke,  inches 

8.0 
3-47 

18.0 
7.24 

21.8 

8.67 

8.0 
1.68 

18.0 

3-47 

21.8 

4.20 

38.6 
7.24 

46.3 
8.67 

Number  of  expansions  

Percentage  of  efficiency  

4.8 
56.0 

7-3 
34-6 

8.1 
3i-3 

5-3 
54-8 

7-9 
32-5 

8.6 
30.0 

10.3 
23.0 

ii.  i 

21  .O 

Steam  per  ind.  h.  p.  per  hour,  pounds  

Initial  Condensation. — Subsequently  to  the  preceding 
steam-engine  tests  Major  English  *  made  some  important  experi- 
ments to  determine  the  amount  of  initial  condensation  directly. 

*  Proceedings  of  the  Inst.  of  M.  E.  1887. 


THERMODYNAMICS  OF  THE   STEAM-ENGINE. 

The  experiments  were  made  on  a  portable  engine,  10  inches 
diameter  and  14  inches  stroke,  jacketed  on  the  sides,  but  not  on 
the  ends.  The  connecting-rod  was  disconnected,  the  piston 
was  rigidly  blocked  at  the  end  of  the  cylinder  farthest  from 
the  crank,  and  the  interior  of  the  cylinder  was  completely 
filled  with  wood  and  iron,  as  was  also  the  steam-passage  at 
the  crank  end.  The  port  at  the  crank  end  was  filled  with  a 
brass  plate  scraped  down  to  a  level  with  the  valve-seat.  The 
port  at  the  head  end  was  left  open,  and  the  crank-shaft, 
eccentric,  and  valve  were  driven  by  another  engine.  The  steam- 
pressure  in  the  boiler  was  maintained  uniform  during  a  trial, 
and  the  regulator  was  kept  open.  As  a  consequence,  steam  at 
boiler-pressure  was  alternately  admitted  to  and  exhausted 
from  the  clearance  space  at  the  head  end,  once  each  revolution, 
for  a  time  corresponding  to  a  cut-off  at  seven  tenths  of  the 
stroke. 

Each  experiment  lasted  an  hour,  during  which  time  revolu- 
tions were  noted  by  a  counter,  and  indicator-cards  were  taken. 
The  steam  passing  through  the  engine  under  these  conditions 
was  condensed,  collected,  and  weighed.  Sixty-four  satisfactory 
tests  were  made,  of  which  thirty-five  were  condensing  and 
twenty-nine  non-condensing.  The  steam-pressures  were  about 
45)  3O>  20,  and  10  pounds  above  the  atmosphere;  and  the  num- 
bers of  revolutions  were  130,  100,  70,  and  50  per  minute. 

Let  yl  be  the  density  or  weight  in  pounds  of  one  cubic 
foot  of  steam,  of  the  steam  up  to  the  point  of  cut-off,  and  let 
tl  be  the  temperature ;  let  y0  and  /0  be  similar  quantities  at  the 
time  when  the  exhaust-port  closes. 

Let  M  be  the  weight  of  water  per  revolution  from  the  con- 
denser. This  is  made  up  (i)  of  the  differences  of  the  weights 
of  steam  shown  by  the  indicator  at  cut-off  and  compression, 


in  which  Fft  is  the  volume  in  cubic  feet  of  the  clearance  space, 
including  the  steam-passages  ;  and  (2)  of  the  weight  of  steam 
condensed,  and  not  re-evaporated,  on  the  constant  surface  Se 
square  feet  of  the  clearance,  including  the  steam-passages.  The 


VARIOUS  STEAM-ENGINE    TESTS, 


weight  of  steam  condensed  per  revolution  and  not  re-evapo- 
rated is 


Let  A,  be  the  total  heat  of  steam  at  the  temperature  ^  ,  and 
let  ql  be  the  heat  of  the  liquid  ;  then  the  thermal  units  absorbed 
by  the  clearance  surface  are 


These  several  quantities  are  given  in  Tables  XXIII  and 
XXIV. 

TABLE  XXIII. 
INITIAL  CONDENSATION  IN  JACKETED  CYLINDER  OF  NON-CONDENSING  ENGINE. 


Density  of  steam. 
Lbs.  per  cubic  ft. 

Thermal  units  in 
one  pound  of 

Net  initial  con- 
densation by 

clearance 

surface. 

Thermal  units. 

1887. 

Clearance 
volume. 

Revolu- 
tions 
per 
second. 

Initial. 

Exhaust. 

Steam. 

Water. 

wi  ater 
collec'd 
per 
revolu- 
tion. 

Total 
per 

Per  sq. 
feet  of 
surface 

revolu- 

at one 

tion. 

rev.  per 
second. 

y. 

N 

Vi 

Va 

A, 

« 

M 

C 

~JF~ 

Cubic  ft. 

Revols. 

Lb. 

Lb. 

Units. 

Units. 

Lb. 

Units. 

Units. 

Mayi6  

0.035 

•73 

0.156 

0.043 

"73 

269 

0.0213 

i5-7 

10.3 

May  25  

0.035 

.19 

0.149 

0.042 

1172 

265 

0.0135 

8.9 

6.6 

May  28  

0.035 

.70 

0.148 

0.043 

1172 

265 

0.0160 

II.  2 

7-3 

May  13  

0.035 

•23 

0.148 

0.043 

1172 

265 

0.0240 

I8.4 

10.2 

June  i     .... 

21 

O    I  A6 

1  171 

263 

18.3 

Mayi6  

0.035 

.64 

0.14^ 

o.  146 

0.040 

A  i/J. 

171 

26^ 

0.0161 

"•3 

7-2 

June  2  

0.035 

.92 

0.144 

0.042 

171 

262 

0.0251 

19.6 

9.4 

May  13  

0.035 

.69 

o.  140 

0.043 

170 

260 

0.0170 

12.4 

8.1 

Mayt6  

0.035 

•54 

0.126 

0.040 

168 

254 

0.0147 

10.7 

6.1 

May  14  

0.035 

•32 

O.IlS 

0.041 

167 

248 

0.0150 

"•3 

6-5 

May  25  

.09 

o.  117 

0.040 

166 

247 

0.0098 

6.5 

4-7 

May  28  

0-035 

•65 

0.116 

0.039 

166 

247 

0.0154 

11.7 

7-5 

May  17  

0.035 

.62 

0.115 

0.042 

166 

247 

0.0150 

"•5 

7-3 

June  2  

0.035 

•85 

0.115 

0.039 

166 

247 

0.0225 

18.2 

8.4 

June  i 

1  66 

May  14  

^•O35 

0-035 

•30 

0.104 

0.041 

165 

241 

0.0120 

9.4 
9-o 

5-3 

5-2 

May  17  

0.035 

.66 

0.103 

0.043 

164 

240 

0.0149 

ii.  8 

7.6 

May  25  

0.035 

•  05 

0.095 

0.039 

163 

234 

0.0069 

4.6 

3-3 

May  14  

0-035 

•25 

0.092 

0.040 

163 

233 

O.OIIO 

8.6 

4.8 

May  31  

0-035 

.69 

0.091 

0.041 

162 

232 

0.0124 

9.9 

6-4 

June  i  

0.035 
0.035 
0-035 

:8o 
•71 

0.090 
0.089 
0.089 

0.040 
0.040 
0.041 

162 
161 
161 

231 
230 
230 

O.OIOI 

0.0151 

O.OIO2 

7-7 
12.5 
7-9 

4.2 
5-6 

5-2 

June  2  
May  17  

May  25  

0.035 

.12 

0.071 

0.039 

157 

216 

0.0044 

3-1 

2-3 

May  31  

0.035 

•65 

0.071 

0.040 

157 

216 

0.0074 

5-9 

3-8 

May  31  

0-035 

.19 

0.070 

0.039 

156 

214 

0.0080 

6.4 

3-5 

May  14  

0.035 

.36 

0.068 

0.039 

156 

213 

0.0065 

5-1 

3-o 

May  17  

0.035 

.64 

0.067 

0.040 

1156 

212 

0.0060 

4-7 

3-o 

June  2  

0.035 

•85 

0.066 

0.039 

1156 

212 

O.OoSl 

6.7 

362 


THERMODYNAMICS  OF  THE   STEAM-ENGINE. 


TABLE  XXIV. 
INITIAL  CONDENSATION  IN  JACKETED  CYLINDER  OF  CONDENSING  ENGINE. 


Density  of  steam. 

Thermal  units  in 

Net  initial  con- 

Lbs. per  cubic  ft. 

one  pound  of 

densation  by 

clearance 

surface. 

Thermal  units. 

i887 

Clearance 
volume. 

Revolu- 
tions 
per 
second. 

Initial. 

Exhaust. 

Steam. 

Water. 

Water 
collec'd 
per 
revolu- 

Total 

Per  sq. 
feet  of 
surface 

tion. 

pei- 
revolu- 

at  one 

tion. 

rev.  per 
second. 

K. 

N 

yi 

Ya 

*! 

A 

M 

C 

^~ 

Cubic  ft. 

Revols. 

Lb. 

Lb. 

Units. 

Units. 

Lb. 

Units. 

Units. 

June  13  

0-035 

.69 

0.146 

0.020 

1171 

263 

0.0173 

11.7 

7.6 

June  15  . 

O.O35 

.21 

o.  145 

O.O2O 

1171 

263 

0.0227 

16.6 

9T 

June  10  

0.035 

.80 

0.143 

O.O24 

1171 

£ 

262 

0.0163 

II.  0 

•  * 

7-4 

June  16  

0-035 

•83 

0.143 

0.015 

1171 

262 

0.0257 

19-3 

8.8 

Aug  4 

0.035 

•95 

o.  143 

0.019 

1171 

262 

0.0203 

*4*  5 

IO.2 

Aug.  3..  . 

0.035 

.87 

o.  143 

O.OI2 

1171 

262 

0.0181 

12.3 

57 

July  28  

0.038 
0.038 

.09 
.60 

0.142 
o.  140 

0.028 
O.O23 

1171 
1170 

•262 

261 

0.0233 
0.0154 

17-3 

10.  0 

•  / 

9.0 

6-3 

July  13  

Aug.  ii  

0.038 

•59 

0.140 

O.OlS 

1170 

260 

0.0160 

10.6 

6.6 

Aug  17  

o  038 

.17 

o.  138 

O.O25 

1170 

2CQ 

o  0176 

8  =; 

6-3 

•i    »•    j  
June  15  

0.035 

•13 

0.118 

O.OI7 

1167 

249 

VJ.Wl^U 

0-0193 

°  •  o 

J4-5 

7-7 

June  13  
June  16  

0.035 
0.035 

% 

0.117 
o.  116 

0.019 
O.OI5 

1166 
1166 

247 

246 

0.0168 
0.0199 

12.3 

7-9 

Aug.  3  

0.035 

•85 

0.114 

0.012 

1166 

246 

0.0142 

f:! 

4-5 

June  10  

0.035 

.90 

0.113 

O.Oig 

1166 

246 

0.0107 

6.8 

4-7 

July  13  

0.038 

.61 

O.II2 

O.O2I 

1166 

246 

0.0115 

7-4 

4-7 

Aug.  ii  

0.038 

•13 

O.III 

0.015 

"65 

244 

0.0093 

5-2 

3-8 

July  28  

0.038 

O.  Ill 

0.025 

"65 

244 

0.0137 

9.6 

5-2 

Aug.  ii  

0.038 

'§ 

o.iir 

0.015 

1165 

244 

0.0115 

7-3 

4-7 

June  13  

0.035 

.09 

0.091 

0.016 

1161 

231 

0.0084 

5-4 

3-9 

June  13  
June  16  

0.035 
0.035 

.70 
86 

0.091 
0.091 

0.016 
0.014 

1161 
1161 

.    231 
231 

0.0109 
0.0144 

7-7 
10.9 

5-o 
5-i 

July  26  

0.038 

15 

0.090 

O.O2O 

1161 

231 

0.0149 

"•3 

6.1 

July  28  

0.038 

13 

0.089 

0.017 

1161 

230 

0.0125 

9.1 

4.8 

Aug.  3  

0.035 

81 

0.088 

0.012 

1161 

230 

0.0142 

10.7 

4.8 

Aug.  12  

0.038 

17 

0.087 

0.015 

1161 

230 

0.0087 

5-6 

4.1 

Aug.  12  

0.038 

•65 

0.083 

O.OlS 

1160 

225 

O.OI22 

9.1 

5-8 

June  13  

0-035 

.19 

0.071 

O.OI5 

"57 

216 

O.OO66 

4-3 

3-2 

June  13  
July  26  
July  26  

0.035 

0.038 
0.038 

:5 

.83 

0.070 
0.070 
0.070 

0.014 
0.015 
O.OI5 

1156 
1156 
1156 

215 
215 
215 

0.0094 
O.OII4 
0.0134 

7  ° 
8.8 
10.6 

4.6 
4-7 
4.8 

Aug.  4  

0.035 

.88 

0.066 

0.012 

1156 

213 

0.0130 

10.5 

5-0 

Aug.  12  

0.038 

•  *3 

0.066 

0.014 

1156 

212 

O.Oo6o 

3-8 

2.8 

Aug.  4  

0.035 

•13 

0.065 

O.OI2 

"55 

210 

0.0103 

7-9 

4.2 

Aug.  ii  

0.038 

.70 

0.063 

0.013 

"55 

209 

O.OIO3 

7-9 

5-2 

The  results  of  the  experiments  indicate  that  the  excess  of 
initial  condensation  over  re-evaporation,  in  these  experiments, 
varies  directly  as  the  initial  density  and  inversely  as  the  square 
root  of  the  number  of  revolutions  N",  per  unit  of  time.  Assum- 
ing that  it  varies  also  as  the  surface  (2  square  feet),  the  last 


VARIOUS  STEAM-ENGINE    TESTS. 


363 


column  of  the  tables  gives  the  amount  in  thermal  units  for  one 
square  foot  and  one  revolution  per  second.  The  results  of  the 
experiments  are  also  plotted  in  Fig.  67,  using  thermal  units 


J^'—  Thermal'TJnfts'per  sqnare  foot'of  clearance  surface 

5                    0.05                    0:10                0.15  1». 

Portable  Engine, 
worked  with  and  without 
Condenser 
With  Condenser    o 
Without                 ,< 

'a 

0 
0 

o 

i 

o 

0 

, 

Q_ 

)  0 

o- 

8 

'o 

o 

<9 

0 

0 

0 

o 

C 

0 

X 

« 

»c 
o 

0 

c 

'0 

O 

o 

0.05                        0.10       ,             O.lS.Lb 

Initial  Density  of  Steam,  Ib.per  Cubic  foot, 
divided  by  square  root  of  revolutions  per  second. 

FiG.  67. 


per  square  foot  as  ordinates  and  the  initial  density  divided  by 
the  square  root  of  the  number  of  revolutions  for  abscissae. 

The  average  of  the  whole  series  of  experiments  corresponds 
with  an  excess  of  condensation  over.evaporation,  equivalent  to 
8.2  thermal  units  per  square  foot  of  clearance  surface  for  steam 
at  60  pounds  pressure  absolute. 

Major  English  states  that  these  experiments  and  his  exper- 
iments given  in  Table  XXII,  and  also  the  experiments  on  the 
revenue  steamers,  pages  270,  273,  and  276,  may  be  fairly  repre- 
sented by  the  following  formulae  for  the  excess  of  condensation 
over  re-evaporation  at  any  point  of  the  stroke  of  an  engine. 


364  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

For  Jacketed  Cylinders. 


For  Unjacketed  Cylinders. 


M  =  excess  of  pounds  of  water  condensed  over  re-evapo- 

ration ; 
xr  -\-  q  =  thermal  units  per  pound  of  the  mixture  in  the  cylin- 

der at  any  given  point  of  the  stroke  ; 

A  W  =  heat  equivalent  of  the  work  done  up  to  that  point  ; 
A:  =  total  heat  of  steam  at  cut-off  ; 
y1  =  density  of  steam  at  cut-off  ; 
y0  =  density  of  steam  at  compression  ; 
5  =  surface  of  cylinder,  including  clearance  up  to  the 

given  point  ; 

Sc  =  surface  of  clearance  ; 
N  =  revolutions. 

Willans'  Steam-engine  Tests.  —  In  1887,  Mr.  Peter 
Willans  *  made  a  large  number  of  tests  under  various  circum- 
stances on  an  engine  of  peculiar  form  invented  by  him. 

This  engine  is  represented  by  Fig.  68,  which  gives  a  verti- 
cal section.  It  has  three  single-acting  pistons  of  diminishing 
diameter  on  a  hollow  piston-rod,  which  forms  the  steam- 
passages  and  is  '  provided  with  ports  and  piston  -valves  for 
admitting  and  exhausting  steam  from  the  several  cylinders. 
The  space  below  each  of  the  two  smaller  pistons  and  above 
the  head  of  the  next  larger  cylinder  forms  a  receiver,  into 
which  the  steam  is  exhausted  and  from  which  it  is  drawn 
by  the  cylinder  below.  Below  the  exhaust  space  under  the 
large  piston  is  a  compression  chamber  filled  with  air  to 
insure  a  constant  compression  on  the  piston-rod.  The  piston 

*  Proceedings  Inst.  Civ.  Eng.,  vol.  xciii. 


VARIOUS  STEAM-ENGINE   TESTS. 


365 


4Steam. 


working  in  this  chamber  serves  also  as  the  guide  to  the 
connecting-rod,  which  is  made  dou- 
ble. The  several  valves  are  all  on 
one  rod  in  the  hollow  piston,  and 
are  moved  by  an  eccentric  on  the 
crank-pin  between  the  connecting- 
rod  ends.  The  cut-off  is  effected 
by  the  ports  in  the  hollow  piston- 
rod,  running  past  a  ring  placed  on 
the  cylinder-head,  at  full  piston 
speed,  and  can  be  varied  by  hand 
or  by  a  governor.  During  the 
tests  the  cut-off  was  accomplished 
by  a  fixed  ring  for  each  test. 

The  pressures  in  the  receiver 
spaces  between  the  smallest  cylin- 
der  and  the  intermediate  cylinder, 
and  between  the  intermediate 
cylinder  and  the  largest  cylinder, 
varied  to  such  a  degree  that  there 
were  really  five  stages  of  expan- 
sion in  the  engine  when  running 
nominally  with  triple  expansion, 
and  three  stages  when  running 
compound.  In  Fig.  69  the  dia- 
grams from  the  three  cylinders 
and  the  two  receiver  spaces  are 
combined,  so  as  to  show  the  true  relations  of  volumes  and 
pressures. 

Indicator-diagrams  were  taken  with  a  Crosby  indicator,  and 
in  order  to  get  clear  diagrams  the  main  group  of  experiments 
were  made  at  400  revolutions  per  minute,  but  in  practice  it  is 
the  habit  to  run  at  500  revolutions  per  minute. 

In  comparing  these  tests  it  was  assumed  that  the  work 
theoretically  due  to  the  heat  in  the  steam  was  the  heat  changed 
into  work  by  an  engine  working  on  the  cycle  represented  by 


Scale  3  inches  —  1  foot. 
FIG.  68. 


366 


THERMODYNAMICS  OF   THE  STEAM-ENGINE. 


Fig.  70.     It  was   assumed  that  dry  saturated  steam  was  ad- 
mitted at  the  absolute  pressure  p1  from  a  to  b ;  that  the  steam 


190- 

180-4 

170- 

160- 

150- 


|ioo- 

»    80- 

U- 

^::: 

40- 


10- 


FIG.  69. 

was  expanded  adiabatically  from  b  to  c  till  the  absolute  pressure 
became  j>9  ;  and  that  the  steam  was  exhausted 
against  a  constant  pressure. 

The  efficiency  of  this  cycle  may  be  cal- 
culated  as  follows  :  The  work  of  M  pounds 
of  steam  during  admission  is 


FIG.  70. 


The  work  during  expansion  by  equation  (156),  page  in,  is 
M 


The  work  during  exhaust  is 


VARIOUS  STEAM-ENGINE    TESTS.  367 

The  work  done  by  the  steam  during  the  cycle  is 
M 


M 

--(r1-x^  +  <?,-&)  .....     .    ,    .     (307) 


But  by  equation  (146) 


which,  introduced  into  equation  (307),  gives 


Mr.  Willans  used  770  for  the  mechanical  equivalent  of  heat 
and  461°  for  the  absolute  temperature  of  the  zero  of  the  Fah- 
renheit scale,  and  gives  as  an  approximation  for  equation  (308) 


and  for  the  steam  used  per  horse-power  per  hour 


(3io) 


7^ +7;  4-7^- 


which  may  be  compared  with  equation  (243),  page  180. 

The  best  ratio  of  expansion  was  determined,  for  any  given 
absolute  pressure,  by  aid  of  the  diagram  Fig.  71.  The  abscissae 
represent  volumes,  and  the  ordinates  the  work  calculated  by 
equation  (309).  Ob  represents  the  volume  of  M  pounds  of 
steam  admitted  at  the  absolute  pressure  of  50  pounds,  la 


368 


THERMODYNAMICS  OF   THE  STEAM-ENGINE. 


represents  the  total  work  done  during  the  admission,  of  which 
ib  must  be  expended  in  overcoming  the  back  pressure  during 
exhaust,  leaving  the  useful  work  ab.  The  lines  2ct  $e,  etc.,  rep- 
resent the  total  forward  work  during  admission  and  expansion 
to  2  times,  3  times,  etc.,  the  original  volume,  of  which  the 
portions  2d>  $f,  etc.,  represent  the  work  of  overcoming  the 


FIG.  71. 

back  pressure,  and  the  portions  cd,  ef,  etc.,  represent  the  useful 
work.  The  limit  of  useful  expansion  is  that  at  which  the  use- 
ful work  becomes  a  maximum.  The  line  xy  is  drawn  through 
the  points  on  the  curves  for  the  several  pressures,  beyond  which 
little  or  no  gain  is  obtained  from  further  expansion.  The  dia- 
gram is  for  a  non-condensing  engine  exhausting  against  the 
pressure  of  the  atmosphere,  and  it  is  apparent  that  much  greater 
expansion  would  be  advisable  if  the  engine  were  condensing 
with  a  small  absolute  back  pressure. 

The  nominal  ratio  of  expansion  in  each  test  was  fixed  by 
dividing  the  volume  of  steam  at  the  terminal  pressure,  exhausted 
from  the  low-pressure  cylinder,  by  the  capacity  of  the  high- 


VARIOUS  STEAM-ENGINE    TESTS. 


pressure  cylinder  at  cut-off,  neglecting  clearances.  The  volume 
exhausted  was  assumed  to  be  represented  by  the  line  CB  in 
Fig.  72.  This  line  CB  was  assumed  to  be  0.95  of  the  stroke, 
represented  by  AB. 

During  the  tests  the  power  of  the  engine  was  absorbed  by 
a  dynamo-machine,  the  load  being  adjusted  by  regulating  the 
resistance  in  the  circuit. 

The  feed-water  was  drawn  by  the  feed-pump  from  a  tank 
holding  sufficient  water  for  a  test  and  mounted  on  a  weighing- 
machine.  The  weight  of  the  tank  and  water  was  noted  at  the 


'  Point  of  Cut  Off 


FIG. 


beginning  and  end  of  the  test,  at  which  times  the  suction  of 
the  feed-pump  was  disconnected.  Before  beginning  a  test  the 
water  in  the  boiler  was  raised  above  the  middle  of  the  glass 
water-gauge,  and  the  feed-pump  was  disconnected  while  the 
weight  was  taken.  When  the  water  in  the  glass  gauge  reached 
a  standard  mark  at  about  half  the  height  of  the  water-gauge, 
the  time  of  beginning  the  test  was  noted,  a  counter  was  thrown 
into  gear,  the  feed-pump  was  connected  and  started,  indicator- 
diagrams  were  taken,  and  temperatures  were  read  on  ther- 
mometers. A  few  minutes  before  the  conclusion  of  a  test  the 
water  was  raised  in  the  boiler  about  half  an  inch  above  the 
reference-mark  on  the  glass  gauge,  and  the  feed-pump  was  dis- 
connected and  the  weight  of  the  tank  and  water  was  taken. 
When  the  water  reached  the  reference-mark  on  the  gauge  the 
time  was  noted  as  the  end  of  the  test,  and  the  counter  was 


370  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

thrown  out  of  gear.  The  only  source  of  error  was  the  uncer- 
tainty of  the  height  of  the  water  in  the  glass  gauge,  which  gave 
an  error  not  exceeding  0.25  per  cent. 

The  pressure  in  the  boiler  rarely  varied  two  pounds  in  any 
test.  Three  sets  of  indicator-diagrams  were  taken  each  hour, 
which  were  practically  identical. 

The  largest  cylinder,  nearest  the  crank,  is  called  the  low- 
pressure  or  l.-p.  cylinder ;  the  other  two  cylinders  are  called 
the  high-pressure  or  h.-p.  cylinder,  and  the  h.  h.-p.  cylinder. 
The  main  dimensions  of  the  engine  are  given  in  the  following 
table : 

Willans  Engine. 

Stroke,      . .     .     .       6  in. 

Diameters :  h.  h.-p.  cylinder,  ....       7   " 

h.-p.  cylinder, 10   " 

l.-p.  cylinder,    ...     .     .  14    " 

Net  area:      h.  h.-p.  piston, 34.500  sq.  in. 

under  side  of  same,  .     .     .  31.416      " 

h.-p.  piston, 7I-472      " 

under  side  of  same,  .     .     .  65.973      " 

l.-p.  piston,  ......  141.340      " 

Capacity  of  trunk  clearance:  h.  h.-p.,  .  n.i  cu.  in. 

h.-p.,  .     .  15.0      " 

l.-p.,    .     .  26.0       " 

Capacity  of  cylinder  clearance  :  h.  h.-p.,  14.8      " 

h.-p.,    .  30.0      " 

1.-P,     •  33-6      " 

The  data  and  results  of  the  tests  are  given  in  Tables  XXV 
to  XXXI. 

In  Table  XXV  the  ratio  of  expansion  corrected  is  deter- 
mined by  dividing  the  volume  of  steam  at  the  terminal  pres- 
sure, discharged  from  the  l.-p.  cylinder  by  such  a  volume  of 
steam  at  mean  admission  pressure  as  would  agree  with  the 
steam  shown  Sy  the  indicator  at  the  point  of  cut-off.  This 
method  of  calculating  the  expansions  takes  account  of  steam 


VARIOUS  STEAM-ENGINE    TESTS. 


371 


TABLE   XXV. 
TESTS  ON  WILLANS  ENGINE — SIMPLE,  PRESSURE  VARIED.  ' 


. 

a 

S 

Pressures. 

*—  "nS 

J; 

rT 

Eiw 

"3 

•£ 

*o 

ion  of  trial, 
utes. 

utions  per  re 
n  during  tri; 

of  cut-off  in 
nder. 

of  expansioi 
ected. 

erature  of  ei 
n,  Fahrenhe 

1 
o" 

1 

Ij 

be 

I 

l! 

5  3 

•a 

G 
6 

s-5 

§1 

1* 

£2 

d 
J; 
-0 

c  •"-• 
a  -a 

•~2  c 

75  rt 

o  t^ 

p,a 

D 

"o  * 

C  « 

«J 

rt  .3. 

—  ~ 

>fl 

<=">, 

•s  o 

S  o 

8 

*Z!  -5 

.~  J^  Tt 

S  **-< 

rt.3 

ctf  *t^  .S2 

OS 

3  S 

Jj  S 

o  ° 

rt  O 

D  u 

rt 

JS  o 

a>  es 

Q 

S 

Pi 

& 

CQ 

OQ 

U 

"* 

2 

H 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

Dec.  9... 

1  80 

393-5 

0.604 

1.79 

68 

14.49 

36.25 

40.88 

35-7 

22.1 

14.8 

19.6 

Dec.  6... 

270 

408.4 

0-437 

2.43 

65 

14.46 

51.0 

50.65 

42.8 

20.2 

14.46 

22.62 

Dec.  8.  .  . 

242 

409.1 

3-°9 

65 

14-57 

74.0 

68.67 

58.2 

22.g 

29.14 

Nov.  30.. 
Nov.  30.. 
Dec.  7.  .  . 
Dec.  5... 

169 
1  80 
176 
298 

4°3  -1? 
400.9 

397-7 
406.16 

0.264 
0.2375 
0.216 

3-45 
3-85 
4.22 
4-57 

64 
58 

14.66 
14-75 
14.64 
14.74 

85.0 

97-o 

IIO.O 
122.0 

78.66 
92.65 
98.14 
106.34 

65-4 
76.3 
80.2 
87.1 

22.12 
23-8 
23-6 
23-5 

iS-4 
T5-6 
15-4 
15-0 

31.06 
36-83 
36.87 
38.61 

I 

Steam  per  indicated 
horse-power  per  hour. 

u 

if 

Percentage  of 
total  feed-water 
missing. 

Heat  units 
missing. 

0 

I 

u 

1 
6 

CJ   p., 

d 

d 

d 

i 

. 

J3 
lfc 

s^ 

rt  —  > 
&  wT 

T3    3 

c 

0 

id 
il 

A 

'3*u  ho 

f 

11 

V.   U 

*$ 

0-0 
«j  C 

o;-i 
•s-g-s 

rt    .  C 

i-  d«j 

g^-s 

h  o_c 

|i 

^_o 

CQ 

^y 

|ig 

cS 

0  >% 

<->  w 

<5 

6  h  >> 

2S& 

< 

Ir& 

£3" 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

16.51 
19.77 

706.0 
711.0 

42.76 
35.96 

37-74 
29.03 

34-67 
28.62 

81.08 
79.58 

4.6 
6-5 

11.7 
19.3 

11.7 

20.53 

10.4 
J7-58 

77-213 
126.588 

3-269 

25  51 

830.8 

32.57 

23.92 

23.02 

70  6 

2.7 

26.5 

28.02 

19.26 

200.544 

8.168 

26.8 
31.61 
31.49 
33.55 

795-2 
850.0 
877.7 
874.4 

29  67 
26.89 

27.8 
26.0 

22.62 

2O.  21 

19.7 
18.36 

21.15 

19.24 
18.66 
17.9 

71.6 
71.5 
67  1 

68.8 

8.'o 

I:! 

23-7 
24.8 
31-25 
29.56 

24.1 

23-3 
27.7 
26.7 

19.2 
18.83 
23-44 
21-53 

170.494 
189.140 
244.866 
229.976 

7.048 
7.863 
10.261 

required  to  fill  clearances,  but  not  of  steam  condensed  during 
admission. 

The  cylinder  pressure  during  admission,  column  9,  is  the 
pressure  from  the  indicator-diagrams,  at  a  point  midway  be- 
tween the  beginning  of  the  stroke  and  the  point  of  cut-off. 

The  total  mean  pressure  referred  to  the  low-pressure  cylin- 
der, column  13,  is,  in  Table  XXV,  simply  the  mean  effective 
pressure.  In  the  triple  and  the  compound  tests  it  is  that  mean 
effective  pressure  which,  acting  on  the  large  piston,  would  give 
the  indicated  horse-power  of  the  engine. 


372  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

In  calculating  the  steam  per  horse-power  per  hour  shown 
by  the  indicator,  column  17,  there  are  two  clearance  spaces  to 
be  considered.  One  is  the  passage  in  the  trunk  between  the 
cut-off  ports  and  the  valve-ports,  which  is  filled  from  the  back 
pressure  to  the  pressure  during  admission.  The  other  is  the 
true  cylinder  clearance,  which  is  filled  from  the  pressure  at  the 
end  of  compression  to  the  pressure  during  admission. 

The  steam  per  horse-power  per  hour,  column  18,  is  calcu- 
lated for  the  mean  admission  pressure  by  equation  (310). 

The  percentage  of  efficiency,  column  19,  is  obtained  by 
dividing  the  steam  per  horse-power  per  hour  required  by  a 
perfect  engine  by  the  steam  actually  used  and  weighed  in  the 
tank.  Unless  the  method  of  determining  this  quantity  is 
borne  in  mind  the  results  in  the  tables  are  liable  to  be  mislead- 
ing. 

The  heat  units  missing  at  cut-off,  column  24,  are  calculated 
on  the  assumption  that  all  the  steam  not  accounted  for  by  the 
indicator  at  that  point  is  present  in  the  form  of  water  at  the 
temperature  which  the  steam  then  has. 

The  heat  units  missing  per  stroke,  column  25,  are  inserted 
to  facilitate  the  comparison  between  the  missing  heat  and  the 
changes  of  temperature  and  surface  of  the  cylinder  walls,  which 
are  usually  supposed  to  account  for  it. 

The  columns  added  in  other  tables  are  those  required  by 
the  use  of  the  steam  in  two  or  three  cylinders. 

Discussion  of  Results. — The  tests  made  with  the  large 
cylinder  only,  that  is,  the  simple  tests  given  in  Table  XXV, 
show  a  regular  decrease  in  the  steam  actually  used  per  horse- 
power per  hour,  as  the  steam  pressure  and  the  number  of  ex- 
pansions are  increased  simultaneously,  with  the  revolutions 
nearly  constant  at  400  per  minute.  It  is  notable  that  the  ratio 
of  the  steam  shown  by  the  indicator  at  cut-off  to  the  steam 
used  by  a  perfect  engine  is  nearly  constant,  and  but  little  larger 
than  one.  This,  together  with  the  increased  condensation  and 
re-evaporation,  explains  why  the  percentage  of  efficiency,  so 
called,  should  diminish  as  the  steam  pressure  and  ratio  of  ex- 
pansion increase. 


VARIOUS  STEAM-ENGINE    TESTS. 


373 


TABLE   XXVI. 
TESTS  ON  WILLANS  ENGINE — SIMPLE  SPEED  TESTS. 


, 

d 

V 

a 

Pressure. 

S-J 

i| 

-• 

g 

s'S 

bo 

. 

1 

9 

1 

S    . 

II 

4 

.Q 

£8" 

|1. 

I 

1 

a. 

"S 

rt 

uration  o: 

evolution 
mean  dur 

oint  of  cu 
cylinder. 

atio  of  ex 
corrected 

emperatu 
room,  Fa 

arometric 

0jU 

'o  rt 

£§1 

III 

">>ri  rt 

bsolute,  a 
of  cut-off 

bsolute,  a 
of  stroke. 

can  back 
absolute. 

otal  mean 
referred  t 
piston. 

Q 

Q 

H 

ft 

PC 

H 

CQ 

CQ 

u 

* 

^ 

* 

H 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

[11 

12 

13 

Dec.  6.  .  . 

270 

408.4 

0-437 

2-43 

6.S 

14-46 

51-0 

50.65 

42.8 

20.  2 

14.46 

22.62 

Dec.  7... 

200.6 

0-437 

2-3 

60 

J4-57 

44-o 

49.55 

43-6 

21.7 

15.2 

21.72 

Dec.  6.  .  . 

122 

110.5 

0-437 

2.25 

50 

14.44 

40.25 

49.04 

43-8 

22.  I 

14.7 

23-13 

Dec.  8... 

242 

409.1 

0-339 

3-°9 

65 

14-57 

74.0 

68.67 

58.2 

22.9 

15.4 

29.14 

Dec.  9.. 
Dec.  8... 

152 
127 

205.2 
112.7 

0-339 
0-339 

3.087 
2-99 

66 
68 

14.47 
14.40 

66.5 
62.0 

71.07 
69.1 

60.  i 
60.6 

25.2 
26.8 

I4-65 

32.0 
32-9 

Nov.  30.. 
Nov.  30.. 

180 

118 

400.9 
223.0 

0.264 
0.264 

3-85 
3-74 

58 

14-75 
14.7 

97.0 

84-7 

92.65 

88.46 

76.3 
74-6 

23.8 
23-1 

15-6 
iS-5 

36.83 

Dec.  t... 

178 

122.8 

0.264 

3-72 

66 

J4-93 

80.0 

89.43 

75-6 

27.0 

38.0 

Dec.  5... 

298 

406.16    0.216 

4-57 

14.74 

122.  0 

106.34 

87.1 

23-5 

15.0 

38.61 

Dec.  2... 

119 

223.7 

0.216 

4-46 

14.98 

112.  0 

108.98 

90.0 

28.1 

42.8 

Dec.  5.  .  . 

123 

138.0 

0.216 

4-32 

14.74 

105.4 

108.72 

93-1 

28.4 

15-5 

44-31 

& 

Steam  per  indicated 
lorse-power  p.  hour,  Ibs. 

c 

M 

H 
11 

Percentage  of 
total  feed-water 
missing. 

Heat  units 
missing. 

« 

"8 

J 

8   A. 

T 

idicated  hors 
power. 

eed-water  us 
hour,  Ibs. 

•fcj 

I 

y  indicator  a 
cut-off. 

equired  by 
perfect 
engine. 

ercentage,  ef 

bs.  of  water 
per  hour,  1.- 
chest. 

i£  o> 
tt 

81 

*J  O 

d 

"**"  t/'O 

6  is*>, 

w   M    <-> 

9^. 
•O^'G 

S§^ 

«   U3    O 

er  hour  at  cu 
off. 

er  stroke  at 
cut-off. 

'-' 

h 

PQ 

pq 

M 

OH 

J 

* 

< 

^ 

ft 

OH 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

19.77 

711.0 

35.96 

29.03 

28.62 

79.58 

6-5 

19-3 

20.53 

17-58 

126.588 

5-166 

19.32 

389-4 

41.78 

31  79 

29-  J5 

69.7 

8.0 

23-9 

24-5 

17-57 

85-931 

7  •  T39 

5.47 

251.8 

46.03 

30.16 

29-37 

63.8 

6.0 

34-5 

34-5 

28.8 

79-433 

11.97 

25.51 

830.8 

32.57 

23  92 

23.02 

70.6 

2-7 

26.5 

28.02 

19.26 

200.544 

8.168 

14.05 

483-35 

34  4 

22.55 

22.5 

65.4 

5-o 

34-44 

31.16 

23.07 

I50-973 

12.262 

7.937 

323  -i 

40.7 

22.08 

22.9 

56.2 

5-° 

-45.81 

41.63 

32-71 

I34-384 

19.864 

31.61 

850.0 

26.89 

20.  21 

19.24 

71.5 

8.0 

24.8 

23-3 

18.83 

189.140 

7.863 

16.75 

465-25 

27.77 

20.8 

19.71 

70  9 

24-75 

23.4 

19.52 

101.216 

7-564 

9.98 

339-8 

34.05 

19.61 

19.64 

57.6 

42-5 

37  7 

28.70 

129.168 

17-523 

33.55 
20  49 
13.09 

874.4 
618.6 
408.8 

26  0 
30.19 
31.22 

18.36 
17.41 
17.41 

17.9 
17.68 
17.7 

68.8 
57.66 
56.6 

2.8 

4.0 

29.56 
42-33 
44-5 

26.7 
35-58 
38.2 

21-53 
26.26 
30.65 

229.976 
232-556 
sot.  154 

9.436 
I4-338 
19-475 

374  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Table  XXVI  gives  four  groups*  of  three  tests  each,  made 
on  a  simple  engine  with  the  steam  pressure  and  ratio  of  expan- 
sion nearly  constant,  and  with  the  speed  varying  from  about 
100  to  about  400  revolutions  per  minute.  They  indicate,  a 
regular  and  notable  reduction  of  steam  consumption  per  horse- 
power per  hour,  and  a  regular  gain  of  efficiency,  with  a  marked 
reduction  of  initial  condensation. 

Four  series  of  tests  on  the  engine  running  compound  were 
made  ;  those  in  Table  XXVII  were  made  with  the  speed  con- 
stant and  the  number  of  expansions  varied  according  to  the 
method  shown  in  Fig.  71  ;  those  in  Table  XXVIII  were  made 
with  the  pressure  constant  and  the  ratio  of  expansion  varied  ; 
those  in  Table  XXIX  were  made  in  three  groups,  in  each  of 
which  the  number  of  expansions  .was  constant  and  the  pressure 
varied  ;  those  in  Table  XXX  were  made  in  three  groups  of 
three  each  with  a  varying  speed. 

In  Table  XXVII  the  tests  stated  in  italic  numerals  were 
made  with  the  ratio  of  expansion  given  by  the  expression 

t 

25  ' 

and  the  others  with  the  ratio  of  expansions  determined  by  the 
expression 

/  —  10 


in  which  /  is  the  absolute  steam  pressure.  The  effect  of  this 
variation  of  the  number  of  expansions  is  shown  by  Fig.  73  ;  on 
which  are  plotted  also  the  consumption  for  a  perfect  engine  of 
the  type  represented  by  equation  (308),  and  the  consumptions 
of  the  engine  when  working  simple  and  when  working  com- 
pound. 

As  with  the  simple  tests,  the  consumption  of  steam  per 
horse-power  per  hour  decreases  with  the  simultaneous  increase 
of  steam  pressure  and  expansion  ;  but  the  percentage  of  effi- 
ciency does  not  show  a  notable  falling  off  till  the  boiler-pres- 
sure reaches  130  pounds  above  the  atmosphere. 


VARIOUS  STEAM-ENGINE    TESTS. 


375 


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3/6  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


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VARIOUS  STEAM-ENGINE    TESTS. 


377 


The  reduction  of  initial  condensation  by  compounding  is 
very  noticeable,  and  is  accompanied  by  a  marked  reduction  of 
steam  consumption  at  and  above  80  pounds  absolute.  If  we 
may  assume  that  the  curve  for  the  compound  engine  with 

the  expansion  —  can  be  produced,  it  would  show  that  Com- 
pounding ceases  to  be  of  value  somewhere  between  50  and  60 


100         110        120        130        140 
Steam  Pressure,  (absolute.) 

FIG.  73. 


Ktttt* 


pounds  absolute,  provided  that    the  engine  exhausts  against 
atmospheric  pressure. 

Table  XXVIII  gives  the  results  of  tests  made  with  a, con- 
stant steam  pressure  and  varying  expansion,  while  Table  XXIX 
gives  the  results  of  tests  made  with  fixed  rates  of  expansion 
and  varying  pressure.  A  comparison  of  these  tables  with  Table 
XXVII  shows  that  the  rates  of  expansion  in  the  latter  are  well 
chosen. 


378 


THERMODYNAMICS  OF  THE  STEAM-ENGINE. 


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per  indicated  horse- 
power per  hour. 


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VARIOUS  STEAM-ENGINE    TESTS. 


379 


TABLE  XXIX. 

TESTS  ON  WILLANS  ENGINE,  COMPOUND,  EXPANSIONS  CONSTANT. 

Pressure. 

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380  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 


Heat  units 
missing. 

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o        *?  w.  ^  T" 

ass 

W     M     O>    M 

00    0  0  0 

Percentage  of  total  feed- 
water  missing. 

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s  1  ^  !  IIP 

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10 

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, 

VARIOUS  STEAM-ENGINE    TESTS.  381 

Table  XXX  gives  the  results  of  tests  made  with  speed  vary- 
ing from  100  to  400  revolutions  per  minute.  These  tests,  like 
the  simple  speed  tests,  show  a  reduction  of  steam  consumption 
at  higher  speeds  and  a  corresponding  improvement  in  efficiency, 
due  to  the  reduction  of  initial  condensation.  Mr.  Willans  points 
out  the  fact  that  the  total  initial  condensation  in  a  given  time 
remains  nearly  constant  for  these  compound  speed  tests,  so 
that  doubling  the  speed  of  rotation  reduces  the  initial  conden- 
sation per  stroke  one  half.  He  also  shows  that  this  does  not 
hold  for  the  simple  speed  tests. 

Table  XXXI  gives  the  results  of  tests  made  with  the  en- 
gine running  with  triple  expansion.  A  comparison  with  the 
results  of  Table  XXVII  shows  that  it  is  advisable  to  use  a  com- 
pound engine  below  160  pounds  pressure  absolute,  and  a  triple- 
expansion  engine  above  that  pressure.  The  curves  of  steam 
consumption  in  Fig.  73  indicate  the  same  fact.  In  connection 
with  this  conclusion,  and  when  considering  the  small  degree  of 
expansion  used  even  with  high-pressure  steam,  it  is  to  be  re- 
membered that  this  engine  exhausted  against  the  atmosphere. 
Were  a  condenser  to  be  used  with  the  engine,  and  a  back  pres- 
sure of  two  pounds  absolute  assumed,  then  the  method  used 
for  determining  the  ratio  of  expansion  would  give  results  more 
nearly  in  accord  with  the  ordinary  practice  with  compound  and 
triple-expansion  engines,  which  commonly  work  under  such  con- 
ditions. 

To  determine  the  leakage  past  valves  and  pistons  the  en- 
gine was  blocked  in  various  positions  and  exposed  to  the  pres- 
sure of  steam  from  the  boiler;  meanwhile  the  water-level  in 
the  boiler  was  watched,  and  the  fall  of  water  was  assumed  to 
be  due  to  leakage  and  condensation.  The  largest  amount  thus 
determined  was  15  pounds  per  hour — too  small  a  quantity  to 
be  satisfactorily  determined  in  that  manner. 

A  separator  was  at  first  put  on  the  steam-pipe  for  the  pur- 
pose of  abstracting  the  condensation  in  the  steam-pipe  and 
priming  from  the  boiler,  but  the  entire  amount  collected  in  an 
hour  was  three  pounds,  therefore  the  separator  was  removed. 

Afterwards  calorimeter  tests  of  the  quality  of  the  steam 


382  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 


TABLE  XXX.—  TESTS  ON  WILLANS  ENGINE,  COMPOUND,  SPEED  TESTS. 

Pressure. 

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VARIOUS  STEAM  ENGINE    TESTS. 


383 


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THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


from  the  boiler  were  made  by  blowing  a  hundred-weight  of 
steam  into  the  water  in  the  iron  feed-tank  and  noting  the  rise 
of  temperature.  The  results  of  the  tests  are  given  in  the  fol- 
lowing table,  in  which  w  is  the  weight  of  the  water  in  the  tank 
and  the  water  equivalent  of  the  iron  forming  the  tank,  u  is  the 
weight  of  the  steam  blown  in,  /  is  the  absolute  pressure  of  the 
steam,  and  /3  is  the  corresponding  temperature,  while  tl  and  /„ 
are  the  initial  and  final  temperatures  of  the  water  in  the  tank ; 
x'  is  the  percentage  of  steam  using  Regnault's  value  of  the 
total  heat  of  steam  and  heat  of  the  liquid  ;  x  is  the  percentage 
of  steam  corrected  for  Bosscha's  specific  heat  for  water. 
QUALITY  OF  STEAM  USED  IN  WILLANS  ENGINE. 


Duration 

No. 

/ 

f| 

ft 

*3 

IV 

u 

x^ 

x 

of  blow  in 

Remarks. 

minutes. 

i 

105 

8-505 

24.30 

160.0 

4416 

110.375 

99.82 

99.96 

7.0 

)  Steam  blown  into 

2 

173 

23-35 

39.3 

188.0 

4181 

109.4 

96.87 

96.38 

7.0 

f     warm  water. 

3 
4 
5 
6 

160 
i39 
J54 
162 

ii.  6 

12.00 

15.6 

9.10 

25.81 
25.82 
29.4 
23.32 

184.0 
178  o 
183  o 
185.0 

4919 
4921 

5°32 
4947 

•38 

.2 

o  .97 

.  I 

99.27 
96.29 
99-66 
98.63 

99.488 
96.46 
99.76 
98.93 

8.0 
4.0 
15-0 
4-5 

(  Steam  blown  in 
f     very  fast. 

i  Water  in  boiler 

7 

178 

9.827 

23.501 

188.8 

5263 

.0 

100.4 

100.72 

12.  O 

j      low. 

8 

65 

10.77 

25  *9 

147.8 

4898 

.0 

100.8 

100.48 

9.0 

9 

127 

8.18 

22.73 

174.0 

4836 

no.  8 

99-63 

99-873 

9.0 

The  diagram  in  Fig.  74  is  given  to  show  the  increase  of 


the  pressure  in  the  steam-chest  above  the  boiler-pressure  after 
cut-off,  due  to  the  velocity  and  the  density  of  the  steam  at  160 
pounds  pressure. 


VARIOUS  STEAM-ENGINE    TESTS. 


385 


The  diagrams  in  Figs.  75,  76,  and  77  were  taken  from  the 
compression  chamber  between  the  low-pressure  cylinder  and 
the  engine-shaft.  Fig. 
76  was  taken  under  the 
normal  condition  with  dry 
air  in  the  compression- 
cylinder,  in  which  case  the 
compression  and  expan- 
sion curves  are  scarcely 
distinguishable,  and  are 
both  sensibly  adiabatic. 
Fig.  75  was  taken  when 
a  considerable  amount  of 
water  was  purposely  in- 
jected into  the  compres- 
sion-cylinder, and  Fig.  77 
was  taken  with  steam  in 
the  cylinder  instead  of 
air:  both  indicate  an  ener- 
getic interchange  of  heat 
between  the  fluid  and  the 
cylinder  walls. 

Institute  of  Technol- 
ogy Tests.  —  The  tests 
recorded  in  Table  XXXII 
are  one  series  of  a  large 

number  of  tests  on  simple  g o 

engines,  made  in  the  me-  FIG.  7e. 

chanical  engineering  laboratory  of  the  Massachusetts  Institute 


FIG.  75. 


FIG.  77- 


of  Technology,  and  forming  a  part  of  the  regular  instruction 
in  that  laboratory. 


386 


THERMODYNAMICS  OF  THE   STEAM-ENGINE. 


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VARIOUS  STEAM-ENGINE    TESTS.  387 

The  engine  on  which  the  tests  were  made  is  the  Harris- 
Corliss  engine,  referred  to  on  page  333,  having  a  stroke  of  24 
inches  and  a  diameter  of  8  inches.  The  cylinder  is  covered 
with  hair  felt  and  wood  lagging,  but  is  not  steam-jacketed.  It 
is  supplied  with  steam  containing  from  one  to  two  per  cent  of 
moisture,  as  determined  by  a  large  number  of  tests  with  sev- 
eral kinds  of  calorimeters. 

During  the  tests  the  steam  used  was  condensed  in  a  surface 
condenser,  collected  and  weighed.  Indicator-cards  were  taken 
at  intervals  of  five  minutes  simultaneously,  from  each  end  of 
the  cylinder,  and  at  the  same  time  the  necessary  temperatures 
and  pressures  were  read  and  recorded,  and  the  revolutions  were 
read  on  a  counter.  The  data  in  the  tables  are  determined  from 
the  totals  or  averages  of  the  observations  taken  during  the  test. 

The  errors  of  all  the  instruments  used  during  the  tests  were 
determined  in  the  laboratory,  and  corrections  were  applied  when 
necessary. 

To  insure  regularity  of  results  in  this  series  the  following 
precautions  were  taken:  (i)  the  governor  of  the  engine  was 
disconnected,  the  cut-off  mechanism  was  fixed  by  hand,  and 
the  engine  was  coupled  to  another  engine  to  control  the  speed  ; 
(2)  the  steam-pressure  was  maintained  as  nearly  constant  as 
possible  during  a  single  test ;  (3)  the  tests  of  the  series  all  have 
nearly  the  same  boiler-pressure ;  (4)  during  the  tests  the  throt- 
tle-valve was  wide  open.  A  comparison  of  the  tests  of  this 
series  with  other  tests  on  this  engine,  in  which  some  of  the 
conditions  could  not  be  fulfilled,  shows  clearly  that  all  are  requi- 
site if  definite  results  are  to  be  attained. 

Tests  of  a  Worthington  High-duty  Engine. — In  Table 
XXXIII  are  given  the  data  and  results  of  two  tests  made  by 
Prof.  Unwin  *  on  a  Worthington  high-duty  duplex  compound, 
pumping  engine,  with  compensating  cylinders,  built  by  Messrs. 
Simpson  &  Co.,  Pimlico,  and  operating  at  the  West  Middlesex 
Water-works  at  Hampton. 

The  engines  of  this  type  have  no  fly-wheel  nor  heavy  recip- 
rocating mass,  but  provision  is  made  for  cut-off  and  expansive 
working  of  steam  in  the  high-pressure  cylinder,  by  aid  of  a  pair 

*  Engineering,  Dec.  1888. 


388  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

of  compensating  cylinders  for  each  piston-rod.  The  piston-rod 
carries  the  two  steam-pistons  at  one  end,  the  pump-plungers 
at  the  other  end,  and  near  the  pumps  is  operated  on  by  the 
compensating  cylinders,  which  are  swung  on  trunnions  in 
such  a  manner  that  they  oppose  the  motion  of  the  piston-rod 
at  a  considerable  angle  at  the  beginning  of  the  stroke,  offer  a 
less  resistance  as  the  stroke  proceeds,  till  at  half-stroke  they  are 
opposed  to  each  other  and  mutually  counterbalance  each  other ; 
and  during  the  second  half  of  the  stroke,  when  the  steam  pres- 
sure in  the  cylinder  is  reduced  by  expansion,  they  restore  the 
work  stored  during  the  first  half,  and  help  the  pump  to  com- 
plete its  stroke. 

The  engines  tested  are  used  to  pump  a  large  volume  of 
water  on  a  comparatively  low  lift.  The  high-pressure  pistons 
are  27  inches  in  diameter,  and  the  low-pressure  pistons  are  54 
inches  in  diameter.  The  maximum  stroke  is  44  inches;  during 
the  test  the  stroke  remained  very  constant  at  43  inches.  The 
main  valves  of  each  engine  are  worked  by  the  other  engine, 
but  the  independent  cut-off  valves  of  each  engine  are  worked 
from  its  own  piston-rod,  and  there  is  an  independent  control 
of  the  compression  in  the  high-pressure  cylinder.  The  engines 
work  directly  double-acting  ram-pumps,  the  rams  being  40 
inches  in  diameter,  and  having  the  same  stroke  as  the  steam- 
pistons.  The  valves  are  of  India  rubber,  spring  loaded,  and  the 
slip  is  probably  small.  The  compensating  pistons  are  1 1  inches 
in  diameter,  and  are  loaded  with  an  air-pressure  of  120  pounds 
per  square  inch.  The  pumps  lift  water  from  a  well  communi- 
cating with  the  river  and  deliver  it  through  two  3-feet  mains  to 
reservoirs  nine  miles  distant.  The  head  during  the  tests,  meas- 
*  ured  by  the  difference  of  pressure  in  the  suction-  and  discharge- 
pipes,  was  from  50  ft.  to  65  ft.,  which  head  was  almost  entirely 
expended  in  overcoming  the  friction  in  the  mains. 

The  engine  cylinders  are  completely  jacketed,  and  the  steam 
is  also  taken  through  a  jacketed  reservoir  between  the  cylinders. 
The  jacket-water  was  discharged  through  a  pipe  regulated  by 
a  stop-valve  and  weighed.  The  condensers  are  injection-con- 
densers with  horizontal  air-pumps. 


VARIOUS  STEAM-ENGINE   TESTS.  389 

The  boilers  are  single-flue  Cornish  boilers.  Three  were 
used  during  the  trial  on  October  29th,  and  four  during  the  trial 
on  November  5th  and  6th.  The  boilers  are  28  ft.  long  and 
6  ft.  in  diameter,  with  a  flue  3  ft.  6  in.  in  diameter.  During 
the  trials  on  November  5th  and  6th  the  length  of  the  grate  was 
4  ft.  6  in.,  making  an  area  of  60  sq.  ft. 

The  coal  was  weighed  on  platform  scales  which  had  been 
tested. 

The  feed-water  was  supplied  from  the  delivery  main  at  a 
temperature  of  51  degrees.  The  ordinary  feed  arrangements 
for  supplying  hot  water  from  the  jackets  and  hot-well  were  dis- 
connected. The  feed-water  was  measured  in  a  gauge-tank,  of 
which  the  capacity  was  obtained  by  weighing  in  water  at  the 
temperature  used  during  the  tests,  so  that  no  corrections  for 
temperature  were  required. 

The  feed-tank  delivered  by  a  stop-valve  into  another  tank, 
from  which  a  small  Worthington  feed-pump  delivered  the  water 
into  the  boilers. 

The  Worthington  pump  took  its  steam  from  the  boilers  in 
use  and  exhausted  into  the  tank,  from  which  it  pumped.  The 
whole  of  the  steam  used  was  therefore  recondensed  and  returned 
to  the  boilers. 

Of  the  heat  supplied  by  the  boilers  to  work  the  feed-pump 
nearly  all  was  returned  to  the  boilers.  A  small  portion,  viz., 
that  due  to  the  useful  work  of  pumping  and  that  lost  by  radia- 
tion from  the  tank,  was  no  doubt  lost.  So  far,  a  small  error 
telling  against  the  main  engines  is  introduced. 

The  water-level  at  the  commencement  of  each  trial  in  the 
boiler  gauge-glasses  was  carefully  observed,  and  the  water-level 
was  brought  to  exactly  the  same  marks  at  the  end  of  the  trials. 
Hence  no  correction  has  to  be  made  for  difference  of  level  in 
the  boilers.  The  time  at  which  each  tankful  was  supplied  to 
the  boilers  was  noted,  and  also  the  feed-water  temperature. 
Pyrometer  observations  were  made  in  the  flues  with  two  Mur- 
ries  pyrometers.  During  part  of  the  trial  one  of  these  had  to 
be  used  at  temperatures  near  the  bottom  of  its  scale,  where  the 
indications  are  least  trustworthy.  But  the  mean  of  the  py- 


3QO  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

rometer  readings  is  probably  not  very  incorrect.  Anemometer 
observations  of  the  air  supplied  to  each  boiler  were  taken  every 
half-hour  during  the  twenty-four  hours'  trial,  the  anemometer 
having  been  previously  tested. 

The  air-pump  discharge  was  led  into  a  wooden  tank  with 
stilling  screens.  From  this  it  was  discharged  through  a  sharp- 
edged  circular  orifice  freely  into  the  air.  The  diameter  of  the 
orifice  was  carefully  tested  after  the  trials,  and  the  coefficient 
of  discharge  from  similar  orifices  is  known  to  be  0.599.  The 
temperature  and  head  over  the  orifice  was  noted  every  5  min- 
utes in  the  first  trial,  and  every  7^  minutes  in  the  second.  The 
temperatures  relied  on  in  this  report  were  taken  by  a  fixed 
zero  thermometer,  with  open  scale,  recently  verified  at  Kew. 

As  the  stroke  is  variable,  an  arrangement  of  indicating  fin- 
gers was  attached  to  each  engine,  and  the  length  of  stroke  on 
each  engine  was  noted  every  quarter  of  an  hour. 

The  indicated  power  was  taken  by  four  Richards  indicators, 
chosen  because  they  give  fairly  large  diagrams.  These  indi- 
cators were  sent  to  Kensington  after  the  trials  and  tested  under 
steam.  No  important  error  was  found  at  any  part  of  the  scale 
with  any  of  the  springs.  But  with  the  light  springs  of  the  low- 
pressure  cylinder  indicators  there  was  a  little  frictional  sticking, 
or  else  a  little  slackness  of  the  parallel  motion  joints,  which 
under  a  steady  pressure  introduced  a  small  uncertainty  of  in- 
dication at  one  or  two  points  in  the  range.  Probably  this 
would  be  less  still  when  the  indicator-piston  was  in  motion  as 
when  drawing  a  diagram.  The  indicator-pipes  were  large,  and 
were  clothed.  Diagrams  were  taken  every  half-hour  from  all 
the  cylinders,  so  that  there  were  128  single  diagrams  in  the 
eight  hours'  trial  arid  384  in  the  twenty-four  hours'  trial.  All 
the  eight  hours'  trial  diagrams  were  reduced  by  planimeter; 
also  all  the  diagrams  taken  in  the  first  eight  hours  of  the  twenty- 
four  hours'  trial,  and  half  of  these  taken  subsequently.  The 
conditions  were  so  constant  throughout  the  trial,  and  the  dia- 
grams so  similar,  that  this  was  thought  sufficient. 

The  trial  of  eight  hours'  duration  on  October  29th  was  of 
the  engine  only,  and  no  account  was  taken  of  the  coal  burned. 


VARIOUS  STEAM-ENGINE    TESTS.  391 

During  the  trial  on  the  5th  and  6th  of  November  the  coal  con- 
sumption was  measured  as  well  as  the  efficiency  of  the  engines. 
The  engines,  as  before,  had  been  started  in  the  morning,  but 
before  beginning  the  fires  were  cleaned  and  all  ashes  removed ; 
also  all  coal  was  swept  from  the  boiler-house  floor.  Four  boilers 
were  used,  and  the  fires  were  not  drawn  ;  but  the  condition  of  the 
fires  was  nearly  identical  at  the  beginning  and  at  the  end  of  the 
experiment.  The  fires  were  cleaned  again  about  eighteen  hours 
after  starting,  all  the  clinker  and  ash  removed  being  placed  in 
the  ash-pits.  At  the  end  of  the  trial  the  fires  were  judged  to  be 
on  the  average  slightly  thicker  than  at  the  beginning  of  the 
trial.  The  trial  commenced  at  10.22  A.M.  on  the  5th  and  ended 
exactly  at  10.22  A.M.  on  the  6th.  The  stoke-hole  floor  having 
been  swept  clean  'at  the  beginning  of  the  trial,  the  coal  was 
brought  in  in  quantities  of  about  8  cwt.,  and  the  time  of  finish- 
ing each  lot  was  noted.  The  ash-pits  were  cleaned  before  the 
trial,  and  afterwards  nothing  was  removed  till  the  end  of  the 
trial.  The  fires  were  cleaned  before  the  trial  began,  and  again 
at  4  A.M.  on  Tuesday  morning.  The  fires  were  not  touched 
at  the  end  of  the  trial,  but  the  ash-pits  were  immediately  cleaned, 
and  the  whole  of  the  ashes  were  treated  thus : 

First  the  clinkers,  including  those  removed  from  the  fires  at 
4  A.M.  (six  hours  before  the  end  of  the  trial),  were  separated 
and  weighed.  The  rest  of  the  ashes  were  sifted  through  a  sieve 
with  £-in.  mesh.  All  that  passed  through  the  sieve  is  treated 
as  incombustible  ash,  although  probably  one  third  of  it  is  un- 
burned  carbon.  What  did  not  pass  through  the  sieve  is  treated 
as  unburned  fuel.  Analysis  in  similar  cases  has  shown  that  the 
cinders  retained  by  the  sieve  are  almost  entirely  carbon. 


392 


THERMODYNAMICS  OF  THE  STEAM-ENGINE. 


TABLE  XXXIII. 
DIAMETER  AND  AREAS  OF  CYLINDERS  AND  PUMPS. 


« 

g-s 


Mean. 


H.  P.  cylinder  A:  Back.. . 

front.. . 
H.  P.  cylinder  B:  back. . . 

front.. . 
L.  P.  cylinder  A:  back. . . 

front. .. 
L.  P.  cylinder  B:  back 

front.. . 
Pump-plungers:  back. . . 

front. . 


in. 

26.98 
26.98 
27.02 
27.02 
53-99 
53-99 
54.02 
54-02 
39-90 
39-9° 


in. 

27.02 
27.02 
27.06 
27.06 
54-07 
54-07 
54.10 
54.10 


sq.  in. 


573 

573 

575 

575 
2296 
2296 
2298 
2298.7 
1250.0 
1250.0 


sq. in. 
17.7 
23.8 
17.7 
23-8 

7-o 
17-7 

7-o 
17.7 
16.8 

o 


sq.  in. 

555-7 

549-6 

557-4 

551-3 

2289.2 

2278.5 

2291.7 

2281.0 

1233.2 

1250.0 


553-5 

2285.1 
J  1241.6 


TESTS  OF  ENGINES. 

Date Oct.  29th, 

Duration 8  hours, 

Barometer, 30.166 

..,..., 14.82 

Vacuum, 28.04 

13-77 

Head  pumped  against,   ....  60.63 

Total  double  strokes,      ....  8480 

Length  of  stroke,  minimum,    .     .  41.96 

maximum,  .     .  43.56 

Engine  A:  mean,  .     .     .     .     .    ".  42.83 

"      B:       " 43.00 

Delivery  of  pumps,  not  allowing  )  ^S-SqS 

for  slip,  i  19580000 

Efficiency  of  machine,    ....  0.8434 

Total  feed-water, 41277.8 

"     jacket- water,    .     .     .     *     i  5357 

Double  strokes  per  minute,      .     .  17.67 

Boiler-pressure, 75.2 

Feed-water  per  minute,  ....  85.99 

Jacket-drains  per  minute,   .     .     .  11.16 

Temperature  of  steam,  ....  320.06 

Pressure  on  pump,     .     .     .     .     .  26.27 

"        in  compensators,  .     .     .  120.6 

Mean  pressure  in  H.  P.  cylinders  39-23 

L.P.          "  7-42 


Nov.  5th  and  6th. 

24  hours. 

29.78  in. 

14.627  Ibs.  per  sq.  in. 

27.76  in. 

13.63  Ibs.  per  sq.  in. 
53-68  ft. 
24886 
42.32  in. 
43-56  " 
43-06  " 
43-05  " 

13.407  gallons  per  min. 
I9305504  gallons  in  24h. 
0.8495 
108537  Ibs. 

17.282 

60.29  Ibs.  per  sq.  in. 

75. 37  Ibs. 

11.77  " 

307.36  degrees  F. 

23.26  Ibs.  per  sq.  in. 

120       "      "       " 

32.92 

6.905    "      "       " 


VARIOUS  STEAM-ENGINE    TESTS. 


393 


Temperature  of  injection,   .     .     . 
Temperature     of     air-pump    dis- 
charge,  

Head  over  orifice, 

Air-pump  discharge  per  minute,   . 
Injection-water, 


54 


49.2  degrees 


Engine  A:  H.  P.  back, 
L.  P.      " 

H.  P.  front, 
L.  P.      " 

Engine  B:  H.  P.  back, 
L.  P.      " 

H.  P.  front, 
L.  P.      " 


8i.i8  74  965  degrees 

1.9662  1.7033  ft. 

2777.7  2586  Ibs. 

.     .     .         2702.9  2522.4  Ibs. 

INDICATED    HORSE-POWER. 

;  ;  .  37-78  31.662 

.  .  .  34.19  71.97!  31.145  62.807] 

~.  '.,  .  38.98       rI43<34  34.176 

.  .  .  32.39 


t.'37'J 


128.668 


45-68 
32.13  77.81' 

43-93 
31.17  75.10. 


31.685  6s,86iJ 

35.856 

28.073  63.929] 


27.684   62.92O 


Total  indicated  horse-power,  both  engines,     296.25  255.517 

Lbs. 

Total  feed  per  indicated  horse-power  per  hour,     17.41  17.700 

Jacket-water  ditto, 2.26  2.763 

Used  in  cylinders, 15.15  I4-937 

Heat  absorbed  by  injection-water  per  minute,  .     73,460  64,990 

Heat  retained  by  condensed  steam  per  minute,     1,958  1,519 

Heat  retained  by  jacket-water  per  minute,   .     .     2.958  3,020 

Total, 78,376  69.529 

Heat  rejected   per  indicated  horse-power  per 

minute, 264.6  272.1 

Add  converted  into  work, 42.7  42.7 

Total, , 307.3  314.8 

HEAT   PASSING  THROUGH  ENGINE  PER  MINUTE   PER  INDICATED   HORSE-POWER. 

Thermal  units  from  boiler  in  saturated  steam 

through  cylinders  from  feed  temperature,       .     292.0  287.8 

Latent  heat  of  jacket  steam, 33.6  41.45 

325.6  329.25 

Heat  rejected  in  air-pump  discharge,  ....     254.6  260.24 

Converted  into  work, .    =*     .       42.7               .  42.75 

Radiation  and  error, 28.3  26.26 

325-6  329-25 

Indicated  horse-power, 296.25  255.517 

Pump  horse-power, 249.84  217.06 

Mechanical  efficiency, 8434  .8495 


394  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Feed    per    indicated    horse  -  power    per    hour 

through  cylinders, i$-i$  I4-937  Ibs. 

Feed    per    indicated    horse  -  power    per    hour 

through  jackets 2.26  2.763 

Piston  speed  per  minute 126.4  124  ft. 

TEST  OF  BOILERS. 

Lbs.  Lbs. 

Gross  weight  of  coal  brought  into  boiler-house,    ...  11,180 

Left  on  floor  at  end  of  trial, 99 

Cinders  sifted  out  of  ashes, 132  231 


Total  coal  used, 10,949 

=  456.2  Ibs.  per  hour. 
Lbs. 

The  residue  consisted  of  clinkers, 66 

Incombustible  ashes, 366 

432 

Percentage  of  clinkers  and  ashes, 3.9  Ibs. 

Coal  per  sq.  ft.  of  grate  per  hour, 7.24  Ibs. 

"       "        "      "  heating  surface  per  hour, 0.19    " 

Coal  per  indicated  horse-power  per  hour, 1-785  " 

Water  evaporated  per  pound  of  coal  from  5i°.O7  and  at  307°. 36,  9.914  " 

"      "     "       "      and  at  212°,      .     .     .  11.867  Ibs. 
Estimated  heat  of  combustion  of  coal,  allowing  for  I  per  cent 

of  moisture, 14878  B.  T.  U. 

Thermal  units  per  horse-power  per  minute,  estimated  from  coal 

consumption, 442.6  B.  T.  U. 

Thermal   units   per  horse-power   per  minute,   estimated  from 

boiler  steam  (including  loss  by  radiation), 341.1       " 

Efficiency  of  boiler, 0.77 

Cubic  feet  of  air  per  minute  by  anemometer, 1704 

"        "     "    "     "    pound  of  coal, 225 

Pounds  of  air  per  pound  of  coal, 16.42 

Thermal  Unks 
per  Indicated  Per 

Horse-power  cent. 

Heat  used  and  lost  in  boilers:  per  Hour. 

Total  heat  due  to  coal  used, 26,557  100 


Given  to  steam 20,466  77.1 

Carried  off  in  furnace  gases 2,657  10.0 

Probable  loss  due  to  opening  fire-doors  to  stoke,        .  265  i.o 

Due  to  carbon  in  ashes 284  i.i 

Radiation  and  unaccounted  for,        2,885  10.8 

Duty  of  engine  per  112  Ibs.  of  coal:  24  hours'  trial,  actual,          106,000,000  ft.-lbs. 

8     "          "      estimated,   106,500,000  " 
Corrected  for  difference  of  temperature  of  feed-water  from 

hydrant  and  from  hot-well,        111,500,000  '* 


CHAPTER   XIX. 

FRICTION   OF  ENGINES. 

As  has  been  stated  in  the  discussion  of  the  efficiency  of  the 
steam-engine,  the  economic  value  of  an  engine  is  determined 
by  the  net  or  brake  horse-power,  which  is  the  indicated  horse- 
power less  the  power  used  up  by  the  friction  of  the  mechanism 
of  the  engine. 

Pambour's  Method.  —  It  was  suggested  by  Pambour  that 
the  friction  of  the  engine  could  be  divided  into  two  parts,  one 
of  which  remains  constant  and  can  be  determined  by  indicating 
the  engine  without  a  load,  and  the  other  of  which  increases 
with  the  load  and  is  proportional  to  it.  In  form  of  an  equa- 
tion this  becomes 


(311) 


in  which  F  is  the  horse-power  lost  in  friction  in  the  engine,  P0 
is  the  power  required  to  run  the  engine  unloaded,  and  Pis  the 
useful  or  net  horse-power,  while  f  is  the  coefficient  for  the  in- 
crease of  friction  with  the  load.  The  work  expended  on  the 
air-pump  is  counted  with  the  friction  for  condensing  engines. 
The  efficiency  of  the  mechanism  is 


F+P      P,          P, 

Pi  being  the  indicated  horse-power. 

Rankine  *  states  that  the  unloaded  resistance  P0  is  equiva- 
lent to  a  pressure  of  J-  to  i^  pounds  to  the  square  inch  of  the 
piston;  this  may  be  compared  with  Isherwood's  results  on 
pages  265  and  274.  He  further  states  that  the  value  of  f  =  \, 

*  Steam-engine  and  Other  Prime  Movers,  p.  423. 

395 


396  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

proposed  by  Pambour,  is  corroborated  by  general  experi- 
ence. 

Alsatian  Experiments.— In  Tables  XXXIV,  XXXV,  and 
XXXVI  are  given  the  results  of  tests  made  by  Walther-Meu- 
nier  and  Ludwig,*  to  determine  the  friction  of  a  horizontal 
receiver  compound  engine,  with  cranks  at  right  angles  and  with 
a  fly-wheel,  grooved  for  rope-driving,  between  the  cranks.  The 
piston-rod  of  each  piston  extended  through  the  cylinder  cover 
and  was  carried  by  a  cross-head  on  guides,  and  the  air-pump  was 
worked  from  the  high-pressure  piston-rod.  The  cylinders  each 
had  four  plain  slide-valves,  two  for  admission  and  two  for  ex- 
haust ;  the  exhaust-valves  had  a  fixed  motion,  but  the  admis- 
sion-valves were  moved  by  a  cam  so  that  the  cut-off  was  deter- 
mined by  the  governor. 

The  main  dimensions  of  the  engine  were : 

Stroke, i.i      metres. 

Diameter:  small  piston, O-536  " 

large  piston, 0.800  " 

piston-rods, 0.080  " 

Length  of  connecting-rods,      .'  .     .     .  2.475  " 

Diameter,  air-pump  pistons,    ....  0.360  " 

Stroke,  air-pump, 0.476  " 

Diameter,  fly-wheel, ,     ,  6.6 10  " 

The  engine  during  the  experiments  made  58  revolutions 
per  minute.  The  air-pump  had  two  single-acting  vertical  pis- 
tons. 

Each  experiment  lasted  10  or  20  minutes,  during  which  the 
load  on  the  brake  was  maintained  constant,  and  indicator-dia- 
grams were  taken.  The  experiments  with  small  load  on  the 
brake— i.e.,  No.  9-,  Table  XXXIV  ;  No.  9  and  No.  10,  Table 
XXXV ;  No.  9  and  No.  10,  Table  XXXVI— were  difficult  and 
uncertain. 

The  tests  in  Table  XXXIV  were  made  with  the  engine 
working  compound.  Those  in  Table  XXXV  were  made  with 
the  high-pressure  cylinder  only  in  action  and  with  condensation, 

*  Bulletin  de  la  Soc.  Ind.  de  Mulhouse,  vol.  Ivii.  p.  140. 


FRICTION  OF  ENGINES. 


397 


the  low-pressure  connecting-rod  being  disconnected.  Those 
in  Table  XXXVI  were  made  with  the  high-pressure  cylinder  in 
action,  without  condensation. 

TABLE  XXXIV. 


Tests 

Horse-power  —  Chevaux  aux  vapeur. 

Efficiency. 

Nos. 

Effective. 

Indicated. 

Absorbed  by  the 

engine. 

I 

248.97 

288.45 

39-48 

0.863 

2 

238.92 

276.88 

37-96 

0.862 

3 

228.87 

265.62 

36.75 

0.861 

4 

208  .  78 

243.72 

34-94 

0.856 

5 

188.68 

222.73 

34-05 

0.847 

6 

168.58 

201.48 

32.90 

0.836 

7 

148.48 

180.44 

32.04 

0.822 

8 

128.38 

158.12 

29.74 

O.SlI 

9 

108.28 

136.07 

27.79 

0-795 

TABLE  XXXV. 


Tests. 

Horse-power—  Chevaux  aux  vapeur. 

Efficiency. 

Nos. 

Effective. 

Indicated. 

Absorbed  by  the 

engine. 

I 

128.38 

153-12 

24.74 

0.839 

2 

118.33 

142.— 

23.67 

0.833 

3 

108.28 

130.89 

22.60 

0.827 

4 

98.24 

120.06 

21.82 

0.818 

5 

88.19 

108.96 

20.77 

0.809 

6 

78.14 

97-45 

19.31 

0.801 

7 

68.09 

86.32 

18.23 

0.788 

8 

58.04 

75-72 

17-68 

0.766 

9 

47-99 

65.46 

17-47 

0-733 

10 

37-94 

55-19 

17.25 

0.687 

TABLE  XXXVI. 


Tests. 

Horse-power  —  Chevaux  aux  vapeur. 

Efficiency. 

Nos. 

Effective. 

Indicated. 

Absorbed  by  the 

engine. 

I 

128.38 

145.87 

17.49 

0.880 

2 

II8-33 

135.73 

17.40 

0.871 

3 

108.28 

125.17 

16.89 

0.865 

4 

98.24 

114.44 

16.20 

0.858 

5 

88.19 

103-93 

15.74 

0.848 

6 

78.14 

92.98 

14.84 

0.840 

7 

68.09 

81.97 

13.88 

0.830 

8 

58.04 

71.72 

13.68 

0.809 

9 

47-99 

61.55 

13-56 

0-779 

10 

37-94 

51.34 

13.40 

0.738 

398 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


The  results  of  all  of  the  tests  are  plotted  in  Fig.  78  with 
the  effective  horse-power  for  abscissae,  and  with  the  friction 
horse-power  for  ordinates.  The  lines  may  be  taken  to  rep- 
resent  the  several  series  of  tests,  and  the  points  where  they 
cross  the  vertical  axis  may  be  considered  to  give  P0 ,  the  indi- 
cated power  without  a  load,  which  was  not  determined  directly. 


50 


100 


ABSCISSAE,    EFFECTIVE   HORSEPOWER. 
ORDINATES,    FRICTION    HORSEPOWER. 


150 


FIG.  78. 

Equation  (311)  for  these  several  series  of  experiments  be- 
comes : 

Compound  condensing, 

F  —  20  +  o.offP ; 
Small  cylinder  condensing, 

F=  ii  +  O.I07P; 
Small  cylinder  non-condensing, 

F  =  9  +  o.c62P. 

When  the  engine  ran  with  the  small  cylinder  only  and  with 
condensation,  27.74  horse-power  were  consumed  by  friction  and 


FRICTION  OF  ENGINES. 


399 


other  resistances.  Without  condensation,  and  with  the  air- 
pump  disconnected,  17.49  horse-power  were  thus  consumed. 
The  experimenters  therefore  considered  that  7.25  horse-power 
were  required  to  run  the  air-pump.  From  the  mean  vacuum 
they  estimated  the  power  required  for  the  air-pump  to  be  7.38 
horse-power. 

The  best  efficiency  in  each  case  is  found  with  the  largest 
power.     The  tables  give  : 

Efficiency. 

Compound  condensing, 0.863 

Small,  cylinder  condensing, 0.839 

Small,  cylinder  non-condensing, 0.880 

If  the  power  required  for  the  air-pump  be  deducted  from  the 
power  absorbed  by  the  engine,  then  the  power  used  up  by  the 
friction  of  the  mechanism  divided  by  the  indicated  horse-power 
becomes,  for  the  several  cases : 

Compound  condensing,      .     .     .     .     .     .     .     .     0.113 

Small  cylinder,  condensing,    .     .     .     4    .     .     .     0.115 
Small  cylinder,  non-condensing, 0.12 

In  the  following  table  are  given  the  results  of  other  tests  on 
engines  of  various  types : 

TABLE     XXXVII. 

FRICTION  TESTS  OF   ENGINES. 


L. 

4)  -OS 

/ 

Date. 

Type  of  Engine. 

Names  of  Experimenters. 

fll 

Is 

V)  rj    ^ 

prt    ^ 

ffi  ' 

^  <u 

1864.  -1 

Single  cylinder,  beam  with  four  ) 

< 

1867 

valves,  using  superheated  steam,  j 
Woolf,  beam  

Grosseteste,  Hallauer  

191.44 

0.896 

1876  -j 

Horizontal  Woolf  small  cylinder  | 

(Association    Alsacienne;    Wai-  ) 

170.46 

0.891 

1878 

Corliss 

(Association    Alsacienne;    Wai-  1 

|     ther-Meunier,  Keller  f 

1879 

Semi-fixed  compound,  horizontal  .  . 

j  Association    Alsacienne;    Wai-  1 
|      ther-Meunier,  Keller  f 

60. 

0.876 

1  Association    Alsacienne;    Wai-  ) 

1884 

Colman,  horizontal  ...;  

K      ther-Meunier,     Ludwig,     A.  > 

22.26 

0.878 

(      Burghardt  ) 

1884 

Horizontal  portable 

0   86} 

1885 

Compound  horizontal  

(Association    Alsacienne;    Wai-  j 

59.26 

0.896 

j      ther-Meunier,  Ludwig  f 

40O 


THERMODYNAMICS  OF  THE   STEAM-ENGINE. 


Thurston's  Experiments. — As  a  result  of  a  large  number 
of  tests  on  non-condensing  engines,  made  under  his  direction 
or  with  his  advice,  Prof.  R.  H.  Thurston*  concludes  that,  for 
engines  of  that  type,  the  friction  is  independent  of  the  load, 
and  that  it  can,  in  practice,  be  determined  by  indicating  the 
engine  without  a  load. 

TABLE   XXXVIII.    • 
FRICTION  OF  NON-CONDENSING  ENGINE. 
Straight-line  Engine,  8"  X  14"- 


No.  of 
Card. 

Boiler- 
pressure. 

Revolutions. 

Brake  H.  P. 

I.  H.  P. 

Frictional  H.  P. 

I 

50 

332 

4.06 

7.41 

3-35 

2 

65 

229 

4-98 

7.58 

2.60 

3 

03 

230 

6.00 

IO.OO 

4.00 

4 

69 

230 

7.00 

10.27 

3-27 

5 

73 

230 

8.10 

11.75 

3-65 

6 

77 

230 

9.00 

12.70 

3.70 

7 

75 

230 

IO.OO 

14.02 

4.02 

8 

80 

230 

11.00 

14.78 

3.78 

9 

80 

23O 

12.  OO 

15.17 

3.17 

10 

85 

230 

13.00 

15.96 

2.96 

ii 

75 

230 

I4.OO 

16.86 

2.86 

12 

70 

230 

15.00 

17.80 

2.80 

13 

72 

231 

2O.  IO 

22.07 

1-97 

14 

75 

230 

25.00 

28.31 

3-31 

15 

60 

229 

29-55 

33.04 

3.40 

16 

58 

229 

-        34-86 

37-20 

2-34 

.    ,  J7 

70 

229 

39-85 

43-04 

3.19 

18 

85 

230 

45-oo 

47-79 

2.78 

19 

90 

230 

50.00 

52.60 

2.60 

20 

85 

230 

55-00 

57.54 

2-54 

Table  XXXVIII  gives  the  details  of  one  series  of  tests. 
The  friction  horse-power  is  small  in  all  the  tests,  and  the  varia- 
tions are  small  and  irregular,  and  appear  to  depend  on  the 
state  of  lubrication  and  other  minor  causes  rather  than  on  the 
change  of  load.  Much  the  same  result  is  shown  by  the  tests 
given  in  Tables  XXXIX  and  XL,  the  first  on  an  automatic 
cut-off  engine,  and  the  second  on  a  tandem  compound  engine. 

Distribution  of  Friction. — As  a  consequence  of  his  conclu- 
sion in  the  preceding  section,  Professor  Thurston  states  that 


*  Trans,  of  the  Am.  Soc.  of  Mech.  Engr.,  vols.  viii.,  ix.,  and  x. 


FRICTION  OF  ENGINES. 


401 


TABLE   XXXIX. 
FRICTION  WITH  CHANGE  OF  LOAD. 

Automatic  Engine,  12"  X  18". 
Lansing  Iron  Works.     Steam-pressure,  180  pounds. 


No.  of 
Card. 

Revolutions 
per 
minute. 

Total  I.  H.  P. 

Brake  Load. 

Brake  H.  P. 

FrictionalH.P. 

I 

190 

11.20 

O. 

0. 

1  1.  2O 

2 

190 

II.  19 

0. 

O. 

II  .19 

3 

190 

I0.8o 

O. 

O. 

I0.8o 

4 

1  80 

8.27 

O. 

0. 

9.27 

5 

1  80 

8.76 

O. 

0. 

8.76 

6 

182 

13.24 

ii.  5 

2.79 

10.45 

7 

182 

13-55 

II.  5 

2.79 

10.76 

8 

187 

14.60 

21-5 

5-35 

8.25 

9 

187 

16.84 

22.5 

5.6i 

11.23 

10 

1  80 

18.89 

23-5 

7.89 

II.OO 

ii 

192 

19-43 

46.0 

11.78 

7.65 

12 

I92 

20.78 

49.0 

12.54 

8.24 

13 

I92 

21.25 

49.0 

12.54 

8.71 

14 

192 

21.82 

49.0 

12.54 

9.28 

15 

190 

25-05 

72.5 

18.37 

6.68 

16 

192 

25-65 

72.5 

18.56 

7.09 

17 

192 

27.53 

77-5 

19.84 

7-69 

18 

-    185 

36.38 

II5-5 

28.49 

7.89 

19 

I85 

36.94 

120.5 

29.72 

7.22 

20 

1  80 

41.27 

142.0 

34-08 

7.19 

21 

1  80 

41  .61 

142.0 

34.08 

7-53 

22 

1  80 

44.91 

150.5 

36.12 

8.79 

23 

175 

57.44 

210.5 

49.11 

8-33 

24 

175 

58.70 

209.5 

48.89 

9.81 

the  friction  of  an  engine  may  be  found  by  driving  it  from 
some  external  source  of  power,  with  the  engine  in  substantially 
the  same  condition  as  when  running  as  usual,  but  without 
steam  in  its  cylinder,  and  by  measuring  the  power  required  to 
drive  it  by  aid  of  a  transmission  dynamometer.  Extending 
the  principle,  the  distribution  of  friction  among  the  several 
members  of  the  engine  may  be  found  by  disconnecting  the 
several  members,  one  after  another,  and  measuring  the  power 
required  to  run  the  remaining  members. 

The  summary  of  a  number  of  tests  of  this  sort,  made  by 
Prof.  R.  C.  Carpenter  and  Mr.  G.  B.  Preston,  are  given  in 
Table  XLI.  Preliminary  tests  under  normal  conditions  showed 


402 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


TABLE   XL. 

FRICTION  WITH  CHANGE  OF  LOAD. 
Tandem  Compound  Engine,  14"  and  21"  by  20". 


No.  of 
Card. 

Revolutions. 

I.  H.  P.  for 
both  cylinders. 

Brake  Load. 

Brake  H.  P. 

Frictional  H.  P. 

I 

165 

55-86 

123 

27.  12 

28.74 

2 

168 

57-55 

131 

29.26 

28.29 

3 

138 

79-97 

284 

52.15 

27.82 

4 

152 

84.16 

290 

58-8! 

25  35 

5 

168 

73-65 

2O2 

45-25 

28.40 

6 

1  60 

82.08 

257 

54.83 

27.25 

7 

165 

81.36 

252 

55-44 

25.92 

8 

165 

82.26 

244 

53.67 

28.69 

9 

159 

85.44 

289 

61  .27 

24.17 

10 

159 

86.04 

292 

61.90 

24.14 

ii 

183 

51-11 

83 

20.26 

30.85 

12 

174 

68.45 

145 

33-75 

34-70 

13 

1  60 

86.77 

263 

56.11 

30.66 

14 

162 

80.65 

256 

55-28 

25.37 

15 

158 

82.31 

26l 

55-00 

27.31 

16 

1  60 

88.86 

298 

63-57 

25.29 

17 

156 

87.47 

283 

58-85 

28.62 

18 

136 

86.35 

333 

60.38 

25-97 

19 

130 

83-03 

353 

61.  19 

21.84 

20 

156 

29.22 

o. 

o. 

29.22 

21 

150 







22 

156 

27.63 

0. 

0. 

27-63 

23 

158 

29.69 

o. 

o. 

29.69 

24 

IQO 

127.  10 

V 

that  the  friction  of  the  several  engines  was  practically  the  same 
at  all  loads  and  speeds. 

The  most  remarkable  feature  in  this  table  is  the  friction  of 
the  main  bearings,  which  in  all  cases  is  large,  both  relatively 
and  absolutely.  The  coefficient  of  friction  for  the  main  bear- 
ings, calculated  by  the  formula 


/= 


33000  H.  P. 
pen 


is  given  in  Table  XLII.  /  is  the  pressure  on  the  bearings  in 
pounds  for  the  engines  light,  and  plus  the  mean  pressure  on 
the  piston  for  the  engines  loaded  ;  c  is  the  circumference  of  the 
bearings  in  feet ;  n  is  the  number  of  revolutions  per  minute  ; 
and  H.  P.  is  the  horse-power  required  to  overcome  the  friction 
of  the  bearings. 


FRICTION  OF  ENGINES. 


403 


TABLE   XLI. 
DISTRIBUTION  OF  FRICTION. 


Parts  of  Engine. 

Percentages  of  Total  Friction. 

Straight-line  6x12 
Balanced  Valve. 

Straight-line  6"  x  12" 
Unbalanced  Valve. 

ft  to"  Lansing  Iron 
Works—  Traction-  Lo- 
comotive Valve-gear. 

12"  x  18"  Lansing  Iron 
Works  —  Automatic 
Balanced  Valve. 

2i"x2o"  Lansing  Iron 
Works  —  Condensing 
Balanced  Valve. 

47.0 

35-4 

35-0 

41.6 

46.0 

32-9 

25.0 

21.0 

49.1 

21.8 

6.8 
5-4 

5-1 
4.1 

13-0 

Cross  Head  and  Wrist  Pin.   . 

2-5 
5-3 

26.4 
4.0 

22.  0 

9-3 

21.0 

100.  0 

9.0 

12.0 

Total  

100.0 

100.  0 

100.  0 

IOO.O 

TABLE   XLII. 
COEFFICIENT  OF  FRICTION  FOR  THE  MAIN  BEARINGS  OF  STEAM-ENGINES. 


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.04 

206 

*The  12"  X  18"  automatic  engine  was  new,  and  gave,  throughout,  an  ex- 
cessive amount  of  friction  as  compared  with  the  older  engines  of  the  same  class 
and  make. 


404  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  large  amount  of  work  absorbed  by  the  main  bearings 
and  the  large  coefficient  of  friction  appear  the  more  remark- 
able from  the  fact  that  the  coefficient  of  friction  for  car-axle 
journals  is  often  as  low  as  one  tenth  of  one  per  cent,  the  differ- 
ence being  probably  due  to  the  difference  in  the  methods  of 
lubrication. 

The  second  and  obvious  conclusion  from  Table  XLI  is 
that  the  valve  should  be  balanced,  and  that  nine  tenths  of  the 
friction  of  an  unbalanced  slide-valve  is  unnecessary  waste. 

The  friction  of  the  piston  and  piston-rod  are  always  con- 
siderable, but  they  vary  much  with  the  type  of  the  engine,  and 
with  differences  in  handling.  It  is  quite  possible  to  change 
the  effective  power  of  an  engine  by  screwing  up  the  piston-rod 
stuffing-box  too  tightly.  The  packing  of  both  piston  and  rod 
should  be  no  tighter  than  is  necessary  to  prevent  perceptible 
leakage,  and  is  more  likely  to  be  too  tight  than  too  loose. 


CHAPTER  XX. 

COMPRESSED    AIR. 

COMPRESSED  air,  that  is,  air  at  a  pressure  above  that  of  the 
atmosphere,  is  employed  for  transmitting  power  from  a  place 
where  it  is  conveniently  generated  to  places  where  it  is  to  be 
used.  The  air-blast  used  in  the  production  of  iron  and  steel  is 
compressed  air  of  moderate  pressure ;  the  compressors  for  such 
work  are  called  blowing-machines  or  blowers.  Currents  of  air 
at  slightly  greater  pressure  than  that  of  the  atmosphere  are 
used  for  ventilating  mines,  buildings,  ships,  etc.,  and  for  pro- 
ducing a  forced  draught  for  steam-boilers.  Such  currents  are 
commonly  produced  by  fans  or  centrifugal  blowers.  Air-pumps 
differ  from  air-compressors  in  that  they  take  air  from  a  recep- 
tacle in  which  the  pressure  is  less  than  that  of  the  atmosphere, 
compress  it,  and  deliver  it  against  the  pressure  of  the  atmos- 
phere. 

Power  Expended. — The  indicator-diagram  of  an  air-com- 
pressor with  no  clearance  space  is  represent- 
ed by  Fig.  79.  Air  is  drawn  in  at  atmos- 
pheric pressure  in  the  part  of  the  cycle  of 
operations  represented  by  dc,  in  the  part 
represented  by  cb  the  air  is  compressed,  and 
in  the  part  represented  by  ba  it  is  expelled  FIG.  79. 

against  the  higher  pressure. 

If  /!  is  the  specific  pressure  and  vv  the  specific  volume  of 
one  pound  of  air  at  atmospheric  pressure,  and  /3  and  z>2  corre- 
sponding quantities  at  the  higher  pressure,  then  the  work  done 
by  the  atmosphere  on  the  piston  of  the  compressor  while  air  is 

405 


406  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

drawn  in  is  vlpl.   Assuming  that  the  compression  curve  cb  may 
be  represented  by  an  exponential  curve  having  the  form 

pvn  =  pjj*  =  const., 
then  the  work  of  compression  is 


If  the  compression  is  adiabatic,  then  the  exponent  becomes 

K   =   Cj-  =    1.405. 

The  work  of  expulsion  from  b  to  a  is 


The  effective  work  of  the  cycle  is  therefore 


112) 


Equation  (312)  gives  the  work  done  upon  one  unit  of  weight 
of  air,  and  the  pressures  and  volumes  are  specific  pressures  and 
volumes.  If  A»  v*  >  anc*  ^>  are  tne  pressure,  volume,  and 
temperature  under  standard  conditions,  i.e.,  at  atmospheric 
pressure  and  at  freezing-point,  then  vl  may  be  found  from  the 
equation 

_  R 


T  T 


V 


COMPRESSED  AIR.  407 

It  is  frequently  convenient  to  use,  instead  of  equation  (312), 
one  for  the  mean  effective  pressure  that  may  be  found  by 
dividing  it  by  vl  ,  so  that  we  have 


in  which  p^  and  p^  may  be  stated  in  any  convenient  units,  such 
as  pounds  on  the  square  inch. 

Effect  of  Clearance.  —  The  indicator-diagram  of  an  air-com- 
pressor with  clearance  may  be  represented  by  Fig.  80.  The 
end  of  the  stroke  expelling  air  is  at  #,  and 
the  air  remaining  in  the  cylinder  expands 
from  a  to  </,  till  the  pressure  becomes  equal 
to  the  pressure  of  the  atmosphere  before  the 
next  supply  of  air  is  drawn  in.  The  expan- 
sion curve  ad  may  commonly  be  represented  FlG-  8o> 

by  an  exponential  equation  having  the  same  exponent  as  the 
compression  curve  cb,  in  which  case  the  air  in  the  clearance 
acts  as  a  cushion  which  stores  and  restores  energy,  but  does 
not  affect  the  work  done  on  the  air  passing  through  the  cylin- 
der. The  work  of  compressing  one  unit  of  weight  of  air  in 
such  a  compressor  may  be  calculated  by  aid  of  equation  (312), 
but  the  equation  (313)  for  .the  mean  effective  pressure  cannot 
be  used  directly. 

The  principal  effect  of  clearance  is  to  increase  the  size  of  the 
cylinder  required  for  a  certain  duty  in  the  ratio  of  the  entire 
length  of  the  diagram  in  Fig.  80  to  the  length  of  the  line  dc. 

The  mean  effective  pressure  may  be  calculated  as  for  a 
steam-engine  indicator-card,  taking  account  of  compression 
and  expansion  as  shown  in  Fig.  80,  or  the  mean  effective 
pressure  found  by  equation  (313)  may  be  reduced  in  proportion 
of  the  line  dc  to  the  length  of  the  diagram  in  Fig.  80.  Or, 
again,  the  mean  effective  pressure  by  equation  (313)  maybe 
used  with  the  volume  of  air  actually  drawn  in  per  minute,  in 
calculating  the  horse-power. 

Cooling  during  Compression.  —  If  heat  is  not  withdrawn 
during  compression,  the  temperature  rises  according  to  the  law 


408  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

for  adiabatic  compression.  When  the  maximum  pressure  /2  is 
moderate,  as  in  blowing-machines,  there  is  ordinarily  no  pro- 
vision made  for  cooling  either  the  air  or  the  cylinder,  and  the 
compression  curve  is  approximately  the  adiabatic  for  air. 
When  the  final  pressure  is  considerable,  as  in  the  use  of  com- 
pressed air  for  transmitting  power,  the  high  temperatures  pro- 
duced without  cooling  become  troublesome,  and,  in  all  but 
small  machines,  some  provision  is  made  for  cooling  the  air,  or 
the  cylinder,  or  both. 

The  cylinder  may  be  cooled  by  a  water-jacket,  and  the  air 
is  at  the  same  time  cooled,  in  some  degree,  by  contact  with 
the  walls  of  the  cylinder. 

The  air  is  most  efficiently  cooled  by  injecting  water  into 
the  cylinder,  or  by  using  water  freely  in  the  cylinder  in  some 
form.  By  this  means  the  final  temperature  of  the  air  is  much 
reduced,  and  the  work  of  compression  is  also  reduced.  An  in- 
convenience may  sometimes  arise  from  the  fact  that  when 
water  is  so  used  the  air  delivered  is  nearly  if  not  quite  satu- 
rated with  moisture. 

Moisture  in  the  Cylinder.  —  If  water  is  not  purposely  in- 
jected into  the  cylinder  of  the  compressor,  the  moisture  in  the 
air  will  depend  on  the  hygroscopic  condition  of  the  air  drawn 
in  by  the  compressor.  Even  if  the  air  should  be  saturated  the 
total  and  the  relative  amount  of  moisture  in  the  cylinder  will 
be  insignificant.  Thus  at  60°  F.  the  pressure  of  saturated 
steam  is  about  £  of  a  pound  on  the  square  inch,  and  the  weight 
of  one  cubic  foot  is  about  0.0008  of  a  pound,  while  the  weight 
of  one  cubic  foot  of  air  is  about  0.08  of  a  pound.  If  the  air  is 
not  saturated  the  vapor  exerts  a  less  pressure  than  saturated 
vapor  at  that  temperature,  and  consequently  follows  the  laws 
of  superheated  steam  ;  even  if  the  vapor  is  at  first  saturated,  it 
is  superheated  by  compression,  and  then  follows  the  same  laws. 
Now  the  adiabatic  equation  for  superheated  steam  has  been 
shown  to  be 


so  that  the  only  effect  of  the  moisture  brought  into  the  cylin- 
der by  the  air  is  to  slightly  diminish  the  exponent  of  the  equa- 


COMPRESSED  AIR.  409 

tion  representing  the  compression  curve.  This  conclusion  is 
probably  valid  when  the  cylinder  is  cooled  by  a  water-jacket. 

When  water  is  used  freely  in  the  cylinder  of  a  compressor, 
the  air  is  cooled  by  contact  with  the  water,  and  by  vaporization 
of  the  water.  The  quantity  of  moisture  in  the  air,  and  conse- 
quently the  weight  of  the  mixture  of  air  and  vapor  in  the 
cylinder,  varies,  and  the  condition  of  the  air  during,  and  at  the 
end  of,  compression  can  be  determined  only  when  the  tem- 
perature, volume,  and  pressure  are  known.  It  is  commonly 
assumed  that  the  air  is  saturated  at  all  times  under  this  con- 
dition. 

Temperature  at  the  End  of  Compression.  —  When  the 
air  in  the  compressor  cylinder  is  dry  or  contains  only  the 
moisture  brought  in  with  it,  it  may  be  assumed  that  the  mix- 
ture of  air  and  vapor  follows  the  law  of  perfect  gases 


T          T,  ' 
which,  combined  with  the  exponential  equation 


gives 

n-i  n-i 

A  "        A  * 


T  T 

*«  *  i 


(314) 


from  which  the  final  temperature  T9  at  the  end  of  compression 
may  be  determined  when  Z1,  is  known. 

When  water  is  used  freely  in  the  cylinder  of  a  compressor 
the  final  temperature  cannot  be  determined  directly.  Even  if 
it  be  assumed  that  the  air  is  always  saturated,  and  if  the  expo- 
nent for  the  exponential  equation  be  known,  it  can  be  deter- 
mined only  by  a  series  of  approximations.  In  experiments 
on  air-compressors  this  temperature  should  be  determined 
directly. 

Contraction  after  Compression. — Ordinarily  compressed 
air  loses  both  pressure  and  temperature  on  the  way  from  the 
compressor  to  the  place  where  it  is  to  be  used.  The  loss  of 


4IO  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

pressure  will  be  discussed  under  the  head  of  the  flow  of  air  in 
long  pipes  ;  it  should  not  be  large,  unless  the  air  is  carried 
long  distances.  This  loss  of  temperature  causes  a  contraction 
of  volume  in  two  ways  :  first,  the  volume  of  the  air  at  a  given 
pressure  is  inversely  as  the  absolute  temperature  ;  second,  the 
moisture  in  the  air,  whether  brought  in  by  the  air  or  supplied 
in  the  condenser,  in  excess  of  that  which  will  saturate  the  air 
at  the  lowest  temperature  in  the  conduit,  is  condensed.  Provi- 
sion must  be  made  for  draining  off  the  condensed  water.  The 
method  of  estimating  the  contraction  of  volume  due  to  the 
condensation  of  moisture  will  be  exhibited  later  in  the  calcula- 
tion of  a  special  problem. 

Interchange  of  Heat.  —  The  interchange  of  heat  between 
the  air  in  the  cylinder  of  an  air-compressor  and  the  walls  of 
the  cylinder  are  the  converse  of  those  taking  place  between 
the  steam  and  the  walls  of  the  cylinder  of  a  steam-engine,  and 
are  much  less  in  amount.  The  walls  of  the  cylinder  are  never 
so  cool  as  the  incoming  air  nor  so  warm  as  the  air  expelled  ; 
consequently  the  air  receives  heat  during  admission  and  the 
beginning  of  compression,  and  yields  heat  during  the  latter 
part  of  compression  and  during  expulsion.  The  presence  of 
moisture  in  the  air  increases  this  effect. 

Volume  of  the  Compressor  Cylinder.—  Let  a  compressor 
making  n  revolutions  or  2n  strokes  per  minute  be  required  to 
deliver  F3  cubic  units  (cubic  feet  or  cubic  meters)  of  air  at  the 
absolute  temperature  T3  and  against  the  absolute  pressure  /3  , 
expressed  in  convenient  units,  such  as  pounds  on  the  square 
inch  or  kilograms  on  the  square  centimeter.  The  volume  of 
air  drawn  in  by  the  compressor  per  minute  at  the  absolute  tem- 
perature r,  and  the  absolute  pressure  /,  can  be  calculated  by 
the  equation 


7-  T     ....... 

*i  *-i 

If  the  compressor  has  no  clearance  the  volume  of  the  cylin- 
der in  cubic  feet  or  cubic  meters  will  be 


~ 
2* 


COMPRESSED  AIR.  411 

If  the  compressor  has  a  clearance,  the  indicator-diagram 
will  be  similar  to  Fig.  80,  and  the  air  in  the  clearance  at  the 
end  of  the  stroke  will  expand  down  to  the  pressure  of  the  at- 
mosphere before  the  supply-valve  will  open.  Let  the  clearance 

be  —  part  of  the  piston  displacement.     The  air  in  the  clearance 

space  will,  after  expansion  from  the  pressure  /2  to  the  pressure 
flt  occupy 


m  p 

part  of  the  piston  displacement.     Consequently  the  piston  dis- 
placement will  be 


expressed  in  cubic  feet  or  cubic  meters. 

The  pressure  in  the  compressor  cylinder  when  air  is  drawn 
in,  is  always  less  than  the  pressure  of  the  atmosphere,  and  when 
the  air  is  expelled  it  is  greater  than  the  pressure  against  which 
it  is  delivered.  From  these  causes  and  from  other  imperfec- 
tions the  compressor  will  not  deliver  the  quantity  of  air  calcu- 
lated from  its  dimensions,  and  consequently  the  volume  of  the 
cylinder  as  calculated,  whether  with  or  without  clearance,  must 
be  increased  by  an  amount  to  be  determined  by  experiment. 

Compound  Compressors.  —  When  air  is  to  be  compressed 
from  the  pressure  pl  to  the  pressure  /2  ,  but  is  to  be  delivered 
at  the  initial  temperature  tl  ,  the  work  of  compression  may  be 
reduced  by  dividing  it  between  two  cylinders,  one  of  which 
takes  the  air  at  atmospheric  pressure  and  delivers  it  at  an  in- 
termediate pressure  //  to  a  reservoir,  from  which  the  other 
cylinder  takes  it  and  delivers  it  at  the  required  pressure  /2, 
provided  that  the  air  be  cooled,  at  the  pressure//,  between  the 
two  cylinders. 

The  proper  method  of  dividing  the  pressures  and  of  propor- 
tioning the  volumes  of  the  cylinders  so  that  the  work  of  com- 


412  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

pression  may  be  reduced  to  a  minimum  may  be  deduced  from 
equation  (312),  when  there  is  no  clearance  or  when  the  clear- 
ance is  neglected. 

The  work  of  compressing  one  pound  of  air  from,  the  pres- 
sure pl  to  the  pressure  //  is 


The  work  of  compressing  one  pound  from  the  pressure 
to       is 


because  the  air  after  compression  in  the  first  cylinder  is  cooled 
to  the  temperature  tl  before  it  is  supplied  to  the  second  cylin- 
der. The  total  work  of  compression  is 


^=^+^  =  A*,~+-2,    (318) 
and  this  becomes  a  minimum  when 


-i 
n 


becomes  a  minimum.     Differentiating  with  regard  to  //,  and 
equating  the  first  differential  coefficient  to  zero,  gives 


-    •      .,...    (319) 

Since  the  air  is  supplied  to  each  cylinder  at  the  tempera- 
ture /,  ,  their  volumes  should  be  inversely  as  the  absolute  pres- 
sures pl  and  //. 

When  air  is  compressed  to  a  very  high  pressure  it  may  be 
advantageous  to  carry  on  the  compression  in  three  or  more  cyl- 
inders successively,  cooling  the  air  on  the  way  from  one  cylin- 
der to  the  next. 


COMPRESSED  AIR.  413 

Fluid  Piston  Compressors. — It  has  been  shown  that  the 
effect  of  clearance  is  to  diminish  the  capacity  of  the  compressor, 
consequently  it  should  be  made  as  small  as  possible.  With 
this  in  view  the  valves  of  compressors  and  blowers  are  com- 
monly set  in  the  cylinder-heads.  Single-acting  compressors 
with  vertical  cylinders  have  been  made  with  a  layer  of  water 
or  some  other  fluid  on  top  of  the  piston,  which  entirely  fills  the 
clearance  space  when  the  piston  is  at  the  end  of  the  stroke. 
An  extension  of  this  principle  gives  what  are  known  as  fluid 
piston  compressors.  Such  a  compressor  commonly  has  a 
double-acting  piston  in  a  horizontal  cylinder  much  longer  than 
the  stroke  of  the  piston,  thus  giving  a  large  clearance  at  each 
end.  The  clearance  spaces  extend  upward  to  a  considerable 
height,  and  the  admission  and  exhaust  valves  are  placed  at  or 
near  the  top,  and  the  entire  clearance  space  is  filled  with  water. 
The  spaces  and  heights  must  be  so  arranged  that  when  the 
piston  is  at  one  end  of  its  stroke,  the  water  at  that  end  shall 
fill  the  clearance  and  cover  the  valves,  and  at  the  other  end  the 
water  shall  not  fall  to  the  level  of  the  top  of  the  cylinder. 
There  are  consequently  two  vertical  fluid  pistons  actuated  by 
a  double-acting  horizontal  piston.  It  is  essential  that  the  spaces 
in  which  the  fluid  pistons  act  shall  give  no  spaces  in  which 
air  may  be  caught  as  in  a  pocket,  and  that  there  are  no  pro- 
jecting ribs  or  other  irregularities  to  break  the  surface  of  the 
water ;  and,  further,  the  compressor  must  be  run  at  a  moderate 
speed. 

The  water  forming  the  fluid  pistons  becomes  heated  and 
saturated  with  air  by  continuous  use,  and  should  be  renewed. 
Cooling  by  a  spray  of  water  during  compression  may  be  com- 
bined advantageously  with  the  use  of  this  form  of  piston. 

Air-pumps  used  with  condensing  engines,  or  for  other  pur- 
poses, may  be  made  with  fluid  pistons  which  are  renewed  by 
the  water  coming  with  the  air  or  vapor.  In  case  the  water  thus 
supplied  is  insufficient,  water  from  without  may  be  admitted, 
or  water  from  the  delivery  may  be  allowed  to  flow  back  to  the 
admission  side  of  the  pump. 


414  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

Displacement  Compressors. — When  a  supply  of  water 
under  sufficient  head  is  available,  air  may  be  compressed  in 
suitably  arranged  cylinders  or  compressors  by  direct  action  of 
the  water  on  air,  compressing  it  and  expelling  it  by  displace- 
ment. 

Rotary  Blowers. — Rotary  blowers  have  one  or  more  rotat- 
ing parts  or  pistons,  so  arranged  that  as  they  rotate  chambers 
of  varying  capacity  are  formed,  which  receive  the  air  at  atmos- 
pheric pressure,  compress  it  and  deliver  it  against  the  higher 
pressure.  No  attempt  is  made  to  cool  the  air,  and  the  clear- 
ance should  be  zero,  so  that  the  work  of  compression  may  be 
calculated  by  equation  (312)  with  n  =  K  =  1.4. 

Fan  Blowers. — The  complete  theory  of  centrifugal  and 
other  rotating  fans  cannot  be  deduced  from  thermodynamics 
alone.  The  work  done  upon  the  air  may,  however,  be  calcu- 
lated as  follows :  Let  the  pressure  and  velocity  of  the  air  ap- 
proaching the  fan  be  pl  and  u^ ,  and  of  the  air  leaving  the  fan 
pi  and  u^ .  Then  the  intrinsic  energy  under  the  initial  and  final 
conditions  will  be,  by  equation  (84), 


and  the  kinetic  energy  of  one  pound  under  the  same  conditions 
will  be 

V'       &' 

so  that  the  work  done  on  the  air  will  be 

2g  K-  i      ' 

or,  substituting  for  v^  from  the  equation  ppf  =  pj>*, 

i 

M>,  (£)"-/,», 

.    .    .   (320) 


COMPRESSED  AIR. 


415 


Tests  of  Compressors. — From  a  large  number  of  tests  on 
fluid-piston  air-compressors  constructed  by  the  Cockerill  Works, 
Seraing,  for  use  at  the  Mont  Cenis  tunnel,  Mr.  John  Kraft* 
has  compiled  the  following  table : 

PERFORMANCE  OF  FLUID  PISTON  IN  COMPRESSORS. 


.S 

4) 

Volume  of  the  cylinder  to 
deliver  on  cubic  meter  of 

Work  of  compression, 
kilogrammeters. 

Friction  of  pis- 
ton and  piston- 

*} 

Absolute  pressx 
atmosphere. 

Required  to 
compress  air 
drawn  in,  at 
constant  tem- 
perature. 

Required  to 
compress  con- 
tents of  cylin. 
at  constant 
temperature. 

Actual  work 
from  indica- 
tor-diagram. 

Loss  from  heat- 
ing in  per 
cent  of  col- 
umn 6. 

Efficiency  of  tl 
compressor. 

Volume  of 
air  drawn 
in  cubic 
meters. 

Piston  dis- 
placement, 
cubic 
meters. 

Loss  of  vol. 
in  per  cent 
of  piston 
displacem't. 

Work  applied 
to  compres- 
sor through 
dynamomet 

Friction  in 
per  cent  of 
column  7. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

2 

3 

2 

3 

2.222 

3-333 

10 

10 

14320 
34046 

15912 
37829 

17185 
43503 

8 
15 

26293 
52204 

53 

20 

0-544 
0.652 

4 

4 

4-444 

IO 

57282 

63646 

70376 

20 

89360 

17 

0.647 

5 

5 

10 

83127 

92364 

113608 

23 

124969 

10 

0.665 

6 

6 

6.666 

10 

111053 

123393 

155675 

26 

171023 

10 

0.649 

The  first  column  gives  the  absolute  pressure  of  the  com- 
pressed air  delivered  by  the  compressor  in  atmospheres.  The 
second  column  gives  the  volume  of  air  that  must  be  drawn  in 
by  the  compressor  to  deliver  one  cubic  meter,  on  the  assump- 
tion that  the  air  is  cooled  after  compression  to  the  original 
temperature.  The  third  column  gives  the  piston  displace- 
ment actually  required  ;  this  is  larger  than  the  volume  in  col- 
umn 2,  because  (a)  the  pressure  in  the  cylinder  while  the  cylin- 
der is  filling  is  less  than  that  of  the  atmosphere ;  (b)  the  air  is 
heated  as  it  is  drawn  into  the  cylinder;  (c)  the  water  forming 
the  fluid  piston  absorbs  air  at  high  pressures  and  gives  it  up  at 
low  pressures ;  (d)  some  water  is  injected  at  each  stroke ;  (e) 
the  air  during  expulsion  has  a  higher  pressure  in  the  cylinder 
than  that  against  which  the  air  is  expelled.  The  total  loss 
from  this  source,  set  down  in  column  4,  was  determined  by 
numerous  experiments.  Column  5  gives  the  work  that  would 
be  required  to  deliver  one  cubic  meter  of  air  if  there  were  no 
loss  or  imperfection,  and  if  thexair  were  maintained  at  the  origi- 
nal temperature  during  compression.  Column  6  gives  the  work 


*  Revue  universelle  des  Mines,  2  S6rie,  Tome  vi.  p.  301. 


THERMODYNAMICS  OF  THE   STEAM-ENGINE. 


required  on  the  assumption  that  ten  per  cent  of  the  piston  dis- 
placement is  lost.  Column  7  gives  the  indicated  work  done  on 
the  contents  of  the  cylinder  for  each  cubic  meter  of  air  deliv- 
ered. The  loss  from  the  failure  to  prevent  heating  during 
compression  is  given  in  column  8.  Column  9  gives  the  work 
expended  on  the  compressor  for  each  cubic  meter  of  air  deliv- 
ered, determined  by  experiments  on  a  Prony  brake.  The  loss 
from  friction  in  per  cent  of  the  indicated  work  is  given  in  col- 
umn 10.  Column  1 1  gives  the  ratio  of  column  5  to  column  9, 
which  is  the  efficiency  of  the  compressor  if  it  is  required  to  de- 
liver air  at  the  original  temperature. 

For  convenience,  Mr.  Kraft  gives  the   distribution  of  the 
work  applied  to  the  compressor  in  the  following  table : 

DISTRIBUTION   OF   WORK   APPLIED   TO   AIR-COMPRESSOR. 


Pressure 

Loss  from 

Loss  from 

in 
Atmospheres. 

Useful  Work. 

Heating  during 
Compression 

Imperfections  of 
Cycle. 

Loss 
from  Friction. 

i. 

2. 

3- 

4- 

5- 

2 

0-544 

0.0485 

o  .  0600 

0.3465 

3 

0.652 

0.1087 

0.0724 

0.1666 

4 

0.647 

0.1427 

0.0712 

0   1434 

5 

0.665 

0.1702 

0.0732 

0.0903 

6 

0.649 

0.1880 

o  0720 

O.OgiO 

Pernolet*  gives  the  following  test  of  a  blowing-engine  used 
to  produce  the  blast  for  Bessemer  converters  at  Creusot.  The 
engine  was  a  two-cylinder  horizontal  engine,  with  the  cranks 
at  right  angles.  The  piston-rod  for  each  cylinder  extended 
through  the  cylinder-head,  and  actuated  t  a  double-acting  com- 
pressor. The  dimensions  were : 

Diameter,  steam-pistons, 1.2  meters. 

"          air-pistons, 1.5       " 

Stroke, 1.8       " 

Diameter  of  fly-wheel, 8.0      " 


*  L'Air  ComprimS,  1876. 


COMPRESSED  AIR.  417 

At  28  revolutions  per  minute  the  following  results  were 
obtained : 

Indicated  horse-power  of  steam-cylinders,    .     .     .     .     .  1082 
"                  "            of  air-cylinders,     .     .     .     ...       999 

Efficiency, «     ...    •     •     »  ......  0.92 

Temperature  of  air  admitted, *     •     •  IO°C. 

"    "    delivered, ,.     .  60°  C. 

Pressure  of  air  delivered,  meters  of  mercury  above  the 

atmosphere, .     .     .     .     .     .     .      1.2 1 

Pressure  of  air  in  supply-pipe,  meters  of  mercury  below 

the  atmosphere, '  . .  ,     .     .  0.023 

At  25  revolutions  there  was  no  sensible  depression  of  pres- 
sure in  the  supply-pipe. 

The  air  from  such  a  blowing-engine  probably  suffers  little 
loss  of  temperature  after  compression. 

Air-pumps. — The  feed-water  supplied  to  a  steam-boiler 
usually  contains  air  in  solution,  which  passes  from  the  boiler 
with  the  steam  to  the  engine  and  thence  to  the  condenser.  In 
like  manner  the  injection-water  supplied  to  a  jet  condenser 
brings  in  air  in  solution.  Also,  there  is  more  or  less  leakage  of 
air  into  the  cylinder  communicating  with  the  condenser,  and 
into  the  exhaust-pipe,  or  the  condenser  itself.  An  air-pump 
must  therefore  be  provided  to  remove  this  air  and  to  maintain 
the  vacuum.  The  air-pump  also  removes  the  condensed  steam 
from  a  surface  condenser,  and  the  mingled  condensed  steam 
and  injection-water  from  a  jet  condenser.  If  no  air  were 
brought  into  the  condenser,  the  vacuum  would  be  maintained 
by  the  condensation  of  the  steam  by  the  injection,  or  the  cool- 
ing water,  and  it  would  be  sufficient  to  remove  the  water  by  a 
common  pump ;  which,  with  a  surface  condenser,  might  be  the 
feed-pump. 

The  weight  of  injection-water  per  pound  of  steam,  calcu- 
lated by  the  method  on  page  196,  will  usually  be  less  than  20 
pounds,  but  it  is  customary  to  provide  30  pounds  of  injection- 
water  per  pound  of  steam,  with  some  method  of  regulating  the 
quantity  delivered. 


4i8 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


It  may  be  assumed  that  the  injection-water  will  bring  in 
with  it  one  twentieth  of  its  volume  of  air  at  atmospheric  pres- 
sure, and  that  this  air  will  expand  in  the  condenser  to  a  volume 
inversely  proportional  to  the  absolute  pressure  in  the  con- 
denser. The  capacity  of  the  air-pump  must  be  sufficient  to 
remove  this  air,  and  the  condensed  steam  and  injection-water. 

An  air-pump  for  use  with  a  surface  condenser  may  be 
smaller  than  one  used  with  a  jet  condenser.  In  marine  work  it 
is  common  to  provide  a  method  of  changing  a  surface  into  a 
jet  condenser,  and  to  make  the  air-pump  large  enough  to  give 
a  fair  vacuum  in  case  such  a  change  should  become  advisable 
in  an  emergency. 

Seaton*  states  that  the  efficiency  of  a  vertical  single-acting 
air-pump  varies  from  0.4  to  0.6,  and  that  of  a  double-acting 
horizontal  air-pump  from  0.3  to  0.5,  depending  on  the  design 
and  condition  ;  that  is,  the  volume  of  air  and  water  actually 
discharged  will  bear  such  ratios  to  the  displacement  of  the 
pump. 

He  also  gives  the  following  table  of  ratios  of  capacity  of 
air-pump  cylinders  to  the  volume  of  the  engine  cylinder  or 
cylinders  discharging  steam  into  the  condenser : 

RATIO   OF   ENGINE   AND   AIR-PUMP   CYLINDERS. 


Description  of  Pump. 

Description  of  Engine. 

Ratio. 

Single-acting  vertical 

Jet-conden 
S  r'.ce- 

Tw- 

Surface- 

Jet-conden 
Surface- 
Jet- 
Surface- 

sing,  expansion  i£  to  2 

"               tj  tO  2 

3  to  5 
3  to  5 
compound    
ing,  expansion   i-J  to  2 

ij  tO  2 

3  to  5 
3  to  5 
compound      .... 

6  to    8 
8  to  10 

10  to  12 
12  tO  15 

15  to  18 
10  to  13 
13  to  16 
16  to  19 
19  to  24 
24  to  28 

<t                  « 

«                  « 

«                  « 

Double-acting  horizontal.  . 
i  <                    « 
«                    « 
«                    <  < 
«                    « 

Calculation  of  an  Air-compressor. — Let  it  be  assumed 
that  an  air-compressor  delivers  100  cubic  feet  of  air  at  a  pres- 


*  Manual  of  Marine  Engineering. 


COMPRESSED  AIR.  419 

sure  of  50  pounds  by  the  gauge  and  at  80°  F.;  also,  that  the 
temperature  of  the  air  supplied  to  the  compressor  is  60°  F.,  that 
the  pressure  of  the  atmosphere  is  14.7  pounds,  and  that  there 
is  a  loss  between  the  compressor  and  the  point  of  delivery  of 
two  pounds  of  pressure. 

The  compressor  must  draw  in  per  minute 

v\  ^ 

100  X  64.7  X   520-7  ,  .     , 

— — -  —  424  cubic  feet. 

14.7  x  540.7 

The  actual  capacity  of  a  fluid-piston  compressor  is  stated  to 
be  0.9  its  apparent  capacity,  so  that  such  a  compressor  would 
have  for  its  apparent  capacity  per  minute 

424  ^-  0.9  —  471.1  cubic  feet. 

Assuming  20  revolutions  or  40  strokes  per  minute,  the 
piston  displacement  will  be 

471.1  -r-  40  =  1 1. 8  cubic  feet, 

or  the  piston  may  have  a  diameter  of  24J  inches,  and  a  stroke 
of  4  feet. 

A  dry-air  compressor  will  deliver  less  than  the  calculated 
amount  of  air  on  account  of  imperfect  action  of  the  valves, 
heating  of  the  air  as  it  enters,  etc.;  but  there  will  be  no  water 
injected,  and  consequently  none  to  expel.  For  comparison 
with  the  calculation  for  the  fluid-piston  compressor  we  will  as- 
sume the  actual  delivery  to  be  0.92  of  the  calculated  delivery, 
allowing  for  clearance.  Consequently  the  apparent  delivery  of 
a  compressor  taking  424  cubic  feet  per  minute  must  be 

424  -=-  0.92  =  460.9  cubic  feet. 

If  the  clearance  is  0.02  of  the  piston  displacement,  then  the 
air  in  the  clearance  at  66.7  pounds  absolute  pressure  will 
occupy 


42O  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

of   the   piston   displacement   at   14.7   pounds   pressure.      The 
piston  displacement  must  consequently  be 

i  +  0.0589  —  0.02  =  1.0389 

times  the  displacement  for  a  similar  compressor  without  clear- 
ance.    The  piston  displacement  per  minute  will  be 

460.9  X  1.0389  =  478.8  cubic  feet. 

Assuming  the  compressor  to  make  60  revolutions  per  minute, 
the  piston  displacement  will  be 

478.8  -f-  120  —  4  cubic  feet, 

or  the  piston  may  have  a  diameter  of  1  5  J-  inches  and  a  stroke 
of  3  feet. 

The  exponent  of  the  equation  representing  the  compres- 
sion curve  for  the  fluid-piston  compressor  may  be  assumed  to 
be  1.2,  so  that  the  mean  effective  pressure  will  be 


x 


1.2      (  f66.7\  ) 

nn  tte)     -  '  I  =  25-3' 


and  the  indicated  horse-power  will  be 
25.3  X  4/I-I  X  144 


33000 


=  52.0  H.P. 


The  mean  effective  pressure  for  a  dry-air  compressor  with 
out  clearance  will  be 


-7  X 


and  the  indicated  horse-power  will  be 
27.8  X  460.9  X  144 


=  55.9  H.P. 
33000 


COMPRESSED  'AIR.  421 

A  dry-air  compressor  with  a  clearance  will  have  a  larger 
piston  displacement,  but  will  absorb  no  more  power,  since  the 
work  stored  and  restored  by  the  air  in  the  clearance  space  does 
not  affect  the  power  required  to  deliver  the  given  amount  of 
compressed  air. 

According  to  Kraft's  table,  on  page  416,  the  friction  of  an 
air-compressor  for  4J-  atmospheres  is  about  10  per  cent  of  the 
gross  power  expended.  Consequently  the  gross  power  re- 
quired to  produce  100  cubic  feet  of  air  by  use  of  a  fluid-piston 
compressor  is 

52.0  -T-  0.90  =  57.8  H.  P. 

If  the  compressor  is  made  with  the  piston  on  the  same  rod 
as  the  piston  of  a  steam-engine  cylinder,  so  that  engine  and 
compressor  form  one  machine,  then  it  may  be  assumed  that  15 
per  cent  of  the  indicated  horse-power  of  the  engine  will  be  ab- 
sorbed by  the  friction  of  the  machine,  and  the  indicated  horse- 
power of  the  engine  will  be 

52.0  -7-0.85  =  61.2  H.  P. 

The  temperature  of  the  air  delivered  by  the  dry-air  com- 
pressor, found  by  the  equation  (314),  will  be 

1-4  ~  I 


.-./,=  802.  i  -460.7    =  34i°.4F. 

If  the  substance  in  the  cylinder  of  the  fluid-piston  compres- 
sor followed  the  law  of  perfect  gases,  then  for  it  the  final 
temperature  would  be 


(6(5  7\   1.2 
tjji    = 

• .  i,  =  669.9  —  460.7    =  2O9°.2  F. 


422  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

But  the  final  temperature  cannot  be  found  in  this  way,  since 
water  is  vaporized  in  the  cylinder  during  compression  and  the 
weight  of  the  substance  operated  on  is  not  constant.  Now 
one  cubic  foot  of  air  at  the  pressure  of  14.7  pounds  will,  after 
compression,  occupy 


- <-»• 


of  one  cubic  foot.  If  the  temperature  2O9°.2  be  assumed  to 
be  the  final  temperature,  and  it  further  be  assumed  that  the 
air  is  saturated  at  that  temperature  after  compression,  then 
the  pressure  exerted  by  the  vapor  will  be  13.87  pounds,  and 
the  pressure  exerted  by  the  air  will  be 

66.7  —  13.87  —  52.83  pounds. 

But  one  cubic  foot  of  air  at  14.7  pounds  pressure  and  at 
60°  F.  will  at  52.8  pounds  pressure  and  at  209°. 2  F.  occupy 

14.7  x  669.9  _        a 

52.8  X  520.8  -°'3582 

•of  a  cubic  foot.  Consequently  it  cannot  be  that  the  air  after 
compression  is  saturated  with  moisture  at  209°. 2  F. 

Suppose  the  temperature  of  the  moist  air  after  compression 
to  be  165°  F.,  then  the  condition  of  the  air  may  be  found  as 
follows :  The  pressure  exerted  by  the  air  will  be 


14.7  X  625.7 

-~-z  —  62.29  pounds, 
520.7  X  0.2836 


and  the  pressure  exerted  by  the  vapor  of  water  will  be 
66.7  —  62.29  —  4-41  pounds, 

while  the  pressure  of  saturated  vapor  at  that  temperature  is 
5.45  pounds.  The  weight  of  one  cubic  foot  of  superheated 
steam  at  the  pressure  of  4.41  pounds  per  square  inch,  or  635 
pounds  per  square  foot,  and  at  the  absolute  temperature  of 


COMPRESSED  AIR.  423 

625°. 7,  may  be  found  by  aid  of  equation  (184),  for  superheated 
steam,  to  be  0.0118  of  a  pound.  Assuming  the  weight  of  the 
vapor  at  the  temperature  of  165°  F.  to  be  proportional  to  the 
pressure,  gives 

0.01449  X  441 

—  =  0.012  pound, 
5.324 

which  is  a  sufficient  approximation. 

Had  the  temperature  been  assumed  to  be  161°  F.,  a  similar 
calculation  would  give  for  the  pressure  of  the  air  61.88  pounds, 
and  for  the  vapor  4.82  pounds,  while  the  pressure  of  saturated 
vapor  at  that  temperature  is  4.84  pounds ;  that  is,  the  air 
would  be  saturated  with  vapor  at  that  temperature. 

The  greater  part  of  the  vapor  in  the  air  at  the  pressure  of 
52  pounds  by  the  gauge  and  at  165°  F.  will  be  condensed 
before  the  air  arrives  at  the  end  of  the  conduit,  where  the 
pressure  is  supposed  to  be  50  pounds  and  the  temperature  80° 
F.  The  volume  of  air  delivered  per  minute  is 

424  x  0.2836  =  120.2 

cubic  feet,  which  by  the  previous  calculation  contains  0.012 
pound  of  moisture  per  cubic  foot,  or,  in  all, 

120.2  x  0.012  —  1.44  pounds. 
The  100  cubic  feet  at  80°  F.  if  saturated  will  contain 

100  X  0.001553  —  0.16  pound, 

so  that  the  water  condensed  per  minute  is,  for  100  cubic  feet, 
1.44  —  0.16  =  1.28  pounds. 

Had  the  temperature  at  the  point  of  delivery  been  the  same 
as  that  of  the  air  supplied  to  the  compressor,  as  is  common  in 
practice,  then  nearly  all  the  vapor  in  the  air  after  compression 
would  have  been  condensed  and  withdrawn. 

When  necessary,  the  contraction  of  volume  after  compres- 
sion on  account  of  the  loss  of*  temperature  and  accompanying 


424  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

condensation  of  moisture  may  be  calculated  as  follows :  The 
pressure  exerted  by  the  air  was  found  to  be  62.29  pounds,  and 
that  exerted  by  the  vapor  to  be  4.41  pounds.  If  the  moisture 
were  entirely  withdrawn  at  165°,  the  air  would  then  exert  the 
entire  pressure  of  66.7  pounds,  and  its  volume  would  be 

120.2  x  62.29 

gg =  112.3  cubic  feet. 

But  at  the  final  temperature  of  80°  the  pressure  of  saturated 
vapor  is  0.5027  of  a  pound,  so  that  the  air  exerts  a  pressure  of 

50  +  J4-7  —  0.50  =  64.2  pounds, 
and  its  volume  will  be 

112.3  x  540.7  x  64.2 


625.7  X  62.29 


=  IOO  cubic  feet. 


In  this  case  the  calculation  gives,  as  it  should,  the  original 
datum  of  the  problem,  and  the  calculation  is  inserted  to  show 
the  method  only.  Obviously  the  final  volume  of  the  air 
delivered  by  a  given  compressor,  at  a  given  temperature  and 
pressure,  may  be  calculated  from  the  volume  drawn  into  the 
compressor  without  calculating  the  volume  delivered  at  the 
pressure  and  temperature  near  the  compressor. 

If  a  so-called  dry-air  compressor  draws  air  from  the  atmos- 
phere, and  the  air  is  finally  used  at  or  near  the  original  tem- 
perature of  the  atmosphere,  then  that  air  will  ordinarily  be 
saturated.  In  the  problem  given,  the  air  supplied  to  the  com- 
pressor per  minute,  if  half  saturated,  will  contain 

424  x  0.0008104 
^ ?*£  Q.I72 

pound  of  moisture.     If  the  air  is  cooled  again  to  60°,  it  can 
contain,  when  saturated, 

zoo  X  .0008104  =  0.08 1 


COMPRESSED  AIR.  42$ 

pound  of  moisture,  and  the  remainder  will  be  condensed. 
Even  at  the  temperature  of  80°,  100  cubic  feet  of  saturated  air 
will  contain  only 

100  X  0.001553  =0.155 

pound  of  moisture,  so  that  the  air  will,  under  the  suppositions, 

be  saturated,  and  some  moisture  will  be  condensed. 

Compressed-air  Engines.  —  Engines  for  using  compressed 

air  differ  from  steam-engines  only  in  details  that  depend  on  the 

nature  of  the  working  fluid.     In  some  instances  compressed  air 

has  been  used  in  steam-engines  without  any  change  ;  for  ex- 

ample, in  Fig.    8  1    the   dotted    diagram  was  taken   from  the 

cylinder  of  an  engine  using 

compressed    air,  and    the 

dot-and-dash  diagram  was 

taken  from  the  same  end 

of  the  cylinder  when  steam 

was  used  in  it.     The  full 

line  ab  is  a  hyperbola,  and 

the  line  ac  is  the  adiabatic 

line     for     a     gas     drawn 

through  the  intersection  of  the    expansion    lines  of   the   two 

diagrams. 

Power  of  Compressed-air  Engines.  —  The  probable  mean 

effective  pressure  attained  in  the  cylinder  of  a  compressed-air 
engine,  or  to  be  expected  in  a  projected 
engine,  may  be  found  in  the  same  manner 
as  is  used  in  designing  a  steam-engine.  In 
Fig.  82,  the  expansion  curve  I,  2  and  the 
compression  curve  3,  o  may  be  assumed  to  be 

adiabatic  lines  for  a  gas  represented  by  the  equation 


FlG-  8i 


FIG.  82. 


and  the  area  of  the  diagram  may  be  found  in  the  usual  way, 
and  therefrom  the  mean  effective  pressure  can  be  determined. 
Having  the  mean  effective  pressure,  the  power  of  a  given  engine 


426  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

or  the  size  required  for  a  given   power   may  be   determined 
directly. 

Let  the  specific  pressure  and  the  specific  volume  in  the 
supply-pipe  be/3  and  vtt  and  let  the  specific  pressure  and  the 
specific  volume  in  the  exhaust-pipe  be  /4  and  v±  ;  then,  assum- 
ing that  there  are  no  losses  of  pressure  in  the  valves  and 
passages,  that  there  is  no  clearance,  and  that  the  expansion  is 
adiabatic,  the  work  of  one  unit  of  weight  of  air  is 


v  -A*.  =  A*. 


'    •    •    C3*> 
or,  in  terms  of  the  final  pressure  and  volume, 

i/'...    (322) 


When  it  is  more  convenient,  the  mean  effective  pressure 
can  be  obtained  by  aid  of  the  equation 


-r,     .     .;(323) 


in  which  the  pressures  may  be  in  any  convenient  units,  as,  for 
example,  in  pounds  on  the  square  inch. 

If  an  engine  fulfils  all  of  the  above  conditions  except  that 
there  is  a  clearance,  then  equations  (321)  and  (322)  maybe  used 
for  finding  the  work  developed  by  one  unit  of  weight  of  air, 
provided  that  the  clearance  is  filled  by  compression,  with  air  at 
the  admission  pressure  /„  .  The  equation  (323)  for  the  mean 
effective  pressure  cannot  be  used  directly,  but  it  may  be  used 
in  connection  with  the  volume  exhausted  per  stroke  or  per 


COMPRESSED  AIR.  427 

minute,  in  calculating  the  power  of  the  engine.  The  diagram 
from  such  an  engine  will  be  represented  by  Fig.  83,  and  the 
foregoing  statement  may  be  put  in  the  fol- 
lowing form  :  The  actual  mean  effective  pres- 
sure is  the  mean  effective  pressure  by  equa- 
tion (323),  multiplied  by  the  ratio  of  the  line 
tt/to  the  entire  length  of  the  diagram.  It  is 
apparent  that  the  only  effect  of  clearance  FlG-  83- 

is  to  increase  the  size  of  cylinder  required  for  a  given  purpose, 
and  with  it  the  work  lost  in  friction. 

Air  Consumption. — The  air  consumed  by  a  given  com- 
pressed-air engine  may  be  calculated  from  the  volume,  pressure, 
and  temperature  at  cut-off  or  release,  and  the  volume,  tempera- 
ture, and  pressure  at  compression,  in  the  same  way  that  the 
indicated  consumption  of  a  steam-engine  is  calculated ;  but  in 
this  case  the  indicated  and  actual  consumption  should  be  the 
same,  since  there  is  no  change  of  state  of  the  working  fluid. 
Since  the  intrinsic  energy  of  a  gas  is  a  function  of  the  tempera- 
ture only,  the  temperature  will  not  be  changed  by  loss  of 
pressure  in  the  valves  and  passages,  and  the  air  at  cut-off  will 
be  cooler  than  in  the  supply-pipe,  only  on  account  of  the 
chilling  action  of  the  walls  of  the  cylinder  during  admission, 
which  action  cannot  be  energetic  when  the  air  is  dry,  and 
probably  is  not  very  important  when  the  air  is  saturated. 

Final  Temperature. — If  the  expansion  in  a  compressed- 
air  engine  is  complete,  i.e.,  if  it  is  carried  down  to  the  pressure 
in  the  exhaust-pipe,  then,  assuming  that  there  are  no  losses  of 
pressure  in  valves  and  passages,  the  final  temperature  may  be 
found  by  the  equation 


If  the  expansion  is  not  complete,  then  the  temperature  at 
the  end  of  expansion  may  be  found  by  the  equation 

Tr       fVc\K~l 


Tt-\T7l        > (325) 


428  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

in  which  Vc  is  the  volume  in  the  cylinder  at  cut-off  and  Vr  at 
release,  Tr  is  the  absolute  temperature  at  the  end  of  expan- 
sion, and  7*3  is  the  temperature  at  cut-off,  assumed  to  be  the 
same  as  in  the  supply-pipe.  Tr  is  not  the  temperature  during 
back  pressure  nor  in  the  exhaust-pipe.  If  the  exhaust-valve 
is  opened  suddenly  at  release  the  air  will  expand  suddenly,  and 
part  of  the  air  will  be  expelled  at  the  expense  of  the  energy  in 
the  air  remaining — much  as  though  that  air  expanded  behind  a 
piston  and  the  temperature  in  the  cylinder  during  exhaust,  and 
at  the  beginning  of  compression,  may  be  calculated  by  equation 
(325).  The  temperature  in  the  exhaust-pipe  will  not  be  so 
low,  for  the  temperature  of  the  escaping  air  will  vary  during 
the  expulsion  produced  by  sudden  expansion,  and  will  only  at 
the  end  of  that  operation  have  the  temperature  7"4,  while  the 
energy  expended  on  that  air  to  give  it  velocity  will  be  restored 
when  the  velocity  is  reduced  to  that  in  the  exhaust-pipe. 

Volume  of  the  Cylinder. — The  determination  of  the 
volume  of  the  cylinder  of  a  compressed-air  engine,  which  uses  a 
stated  volume  of  air  per  minute,  is  the  converse  of  the  determi- 
nation of  the  air  consumed  by  a  given  engine,  and  can  be  found 
by  a  similar  process.  We  may  calculate  the  volume  of  air  at 
the  pressure  in  the  supply-pipe,  consumed  per  stroke  by  an 
engine  having  one  unit  of  volume  for  its  piston  displacement, 
and  therefrom  find  the  number  of  units  of  volume  of  the  piston 
displacement  for  the  required  engine. 

Interchange  of  Heat. — The  interchanges  of  heat  between 
the  walls  of  the  cylinder  of  a  compressed-air  engine  and  the  air 
working  therein  are  of  the  same  sort  as  those  taking  place 
between  the  steam  and  the  walls  of  the  cylinder  of  a  steam- 
engine  ;  that  is  to  say,  the  walls  absorb  heat  during  admission 
and  compression,  if  the  latter  is  carried  to  a  considerable 
degree,  and  yield  heat  during  expansion  and  exhaust.  Since 
the  walls  of  the  cylinder  are  never  so  warm  as  the  entering  air, 
nor  so  cold  as  the  air  exhausted,  the  walls  may  absorb  heat 
during  the  beginning  of  expansion,  and  yield  heat  during  the 
beginning  of  compression. 

The  amount  of  interchange  of  heat  is  much  less  in  a  com- 


COMPRESSED  AIR. 

pressed-air  engine  than  in  a  steam-engine.  With  a  moderate 
expansion,  the  interchanges  of  heat  between  dry  air  and  the 
walls  of  the  cylinder  are  insignificant.  Moisture  in  the  air  in- 
creases the  interchanges  in  a  marked  degree,  but  does  not  make 
them  so  large  that  they  need  be  considered  in  ordinary  calcu- 
lations. 

Moisture  in  the  Cylinder. — The  chief  disadvantage  in  the 
use  of  moist  compressed  air — and  it  is  fair  to  assume  that  com- 
pressed air  is  nearly  if  not  quite  saturated  when  it  comes  to 
the  engine — is  that  the  low  temperature,  experienced  when 
the  range  of  pressures  is  considerable,  causes  the  moisture  to 
freeze  in  the  cylinder  and  clog  the  exhaust-valves.  The  diffi- 
culty may  be  overcome  in  part  by  making  the  valves  and 
passages  of  large  size.  Freezing  of  the  moisture  may  be  pre- 
vented by  injecting  steam  or  hot  water  into  the  supply-pipe  or 
the  cylinder,  or  the  air  may  be  heated  by  passing  it  through  ex- 
ternally heated  pipes,  or  by  some  similar  device.  In  the  appli- 
cation of  compressed  air  to  driving  street-cars  the  air  from  the 
reservoir  has  been  passed  through  hot  water,  and  thereby 
made  to  take  up  enough  hot  moisture  to  prevent  freezing. 
The  study  of  gas-engines  suggests  a  method  of  heating  com- 
pressed air  which  it  is  believed  has  never  been  tried.  The  air 
supplied  to  a  compressed-air  engine,  or  a  part  of  the  air,  could 
be  caused  to  pass  through  a  lamp  of  proper  construction  to 
give  complete  combustion,  and  the  products  of  combustion 
passed  to  the  engine  with  the  air.  Should  such  a  device  be 
used,  it  would  be  advisable  that  the  temperature  of  the  air 
should  be  raised  only  to  a  moderate  degree  to  avoid  destruction 
of  the  lubricants  in  the  cylinder,  and  the  combustion  at  all 
hazards  must  be  complete,  or  the  cylinder  would  be  fouled  by 
unburned  carbon. 

Compound  Air  Engines.— When  air  is  expanded  to  a 
considerable  degree  in  a  compressed-air  engine  a  gain  may  be 
realized  by  dividing  the  expansion  into  two  or  more  stages  in 
as  many  cylinders,  provided  that  the  air  can  be  economically 
reheated  between  the  cylinders.  The  heat  of  the  atmosphere 
or  of  water  at  the  same  temperature  may  sometimes  be  used 


430  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

for  this  purpose.  It  is  not  known  that  machines  of  this  con- 
struction have  been  used.  If  they  were  to  be  constructed,  the 
practical  advantages  of  equal  distribution  of  work  and  pressure 
would  probably  control  the  ratio  of  the  volumes  of  the  cylinders. 

Calculation  of  a  Compressed-air  Engine.— Suppose  that 
a  compressed-air  engine  has  a  diameter  of  10  inches  and  a 
stroke  of  20  inches,  that  it  makes  100  revolutions  per  minute, 
and  is  supplied  with  air  at  80°  F.  and  at  50  pounds  gauge- 
pressure.  Let  the  cut-off  be  at  one-half  stroke,  the  compression 
at  5  per  cent  of  the  stroke,  and  the  clearance  5  per  cent  of  the 
piston  displacement. 

The  pressure  at  the  end  of  expansion  will  be 


pounds  absolute,  or  11.12  pounds  above  the  atmosphere.     The 
pressure  at  the  end  of  compression  will  be 


=38.8 


pounds  absolute,  or  24.1  pounds  above  the  pressure  of  the  at- 
mosphere. 

The  mean  effective  pressure  will  be 

/»i-°s  dv 
M.  E.  P.  =  64.7  X  0.55  +  647  X  (o-SS)14^    ^  -  147  X  0.95 


.-.  M.  E.  P.  =  32.35  +  20.50  —  13.97  -  1.94  =  36.94. 

If  the  engine  has  large  ports  and  automatic  cut-off  valves 
the  mean  effective  pressure  realized  may  be  assumed  to  be  0.95 
of  that  calculated,  or  it  will  be  about  35  pounds. 

Assuming  the  diameter  of  the  piston-rod  to  be  2  inches,  the 
mean  area  of  the  piston  will  be 

2  X  78.54—3.14 

-  =  77  square  inches. 


COMPRESSED  AIR.  431 

The  horse-power  will  therefore  be 

35  X  77  X  2  X  IPO  X  20  =          l  R  p 
33000  x  12 

If,  further,  the  friction  of  the  engine  is  assumed  to  absorb 
one  tenth  of  the  indicated  horse-power,  the  effective  horse- 
power will  be  \2\. 

The  temperature  of  the  air  at  the  end  of  expansion  will  be 


or  —  42°.  F.    The  temperature  at  the  beginning  of  compression 
may  be  assumed  to  be 


or  —  !o6°  F.  The  influence  of  moisture  in  the  air  and  of  the 
interchanges  of  heat  will  be  to  increase  each  of  these  tempera- 
tures. 

Were  it  desired  to  prevent  freezing  in  the  cylinder,  then  the 
lowest  temperature  must  be  at  least  32°  F.,  and  the  entering 
air  should  have  at  least  the  temperature  of 


X  -  =  703-6, 


or  243°.6  F.     It  is  probable  that  a  less  temperature  than  this 
will  obviate  difficulty  from  freezing. 

The  piston  displacement  of  the  engine  will  be 

-  r—  =  0.891  cubic  foot. 
1720 

The  volume  of  air  caught  in  the  cylinder  at  compression 
will  be  0.089  °f  a  cubic  foot  at  the  pressure  of  14.7  pounds,  and 
at  the  absolute  temperature,  as  calculated,  of  354.1.  At  the 


43 2  THERMODYNAMICS  OF   THE   STEAM  ENGINE. 

temperature  80°  F.,  and  at  64.7  pounds  absolute  pressure,  the 
volume  will  be 

540.7      14.7 

0.089  X  -      -  X  -7—^-  =  0.031  cubic  foot. 
354.1       04.7 

Consequently  the  air  consumed  per  stroke  will  apparently  be 

0.55  x  0.891  —  0.031  —  0.459 

of  a  cubic  foot.  But  the  causes  which  prevent  the  realization 
of  the  mean  effective  pressure  diminish  the  consumption  of 
air,  so  that  the  consumption  per  stroke  may  be  assumed  to  be 

0.95  X  0.459  =  0-436 

of  a  cubic  foot.     The  consumption  per  minute  will  therefore  be 
2  x  ioo  x  0.436  =  87.2  cubic  feet. 

Were  it  required  that  a  compressed-air  engine  should  use 
ioo  cubic  feet  of  air  per  minute,  the  piston  displacement  would 
obviously  be  1.02  cubic  feet,  and  the  indicated  horse-power 
would  be  15.6,  while  the  effective  horse-power  would  be  14. 
Comparing  this  result  with  the  power  expended  on  the  fluid- 
piston  air-compressor,  it  appears  that  the  efficiency  of  the  fluid  is 

15.6  -r-  52.O  =  O.3O, 

while  the  efficiency  of  the  whole  apparatus  for  transferring 
power  is 

14-^57.8  =  0.24. 

Efficiency  of  Compressed-air  Transmission.— The  great 
defect  of  compressed  air  as  a  means  of  transmitting  power,  that 
is,  the  small  per  cent  of  work  realized,  is  exhibited  by  the  pre- 
ceding calculation.  Though  a  greater  efficiency  may  be  at- 
tained by  a  better  choice  of  pressures  and  proportions,  the 
result  will  in  all  cases  be  unsatisfactory.  Compressed  air  for 
this  purpose  is  consequently  employed  only  where  power  for 
compression  is  cheap  and  abundant,  or  where  there  are  special 


COMPRESSED  AIR.  433 

reasons  for  using  air.  As  an  example,  compressed  air  is  used 
in  mining  and  tunnelling  where  the  use  of  steam  would  be 
objectionable.  It  is  suggested  that  compressed  air  may  be  used 
in  operating  cranes  where  hydraulic  power  is  objectionable  from 
the  liability  of  freezing  water-pipes,  and  where  there  is  a 
large  loss  from  condensation  of  steam  in  starting  and  operating 
only  a  short  time. 

Experiments  made  by  M.  Graillot*  of  the  Blanzy  mines 
showed  an  efficiency  of  from  22  to  32  per  cent.  Experiments 
made  by  Mr.  Daniel  at  Leeds  gave  an  efficiency  varying  from 
0.255  to  0.455,  with  pressures  varying  from  2.75  atmospheres  to 
1.33  atmospheres.  An  experiment  made  by  Mr.  Kraft  f  gave 
an  efficiency  of  0.137  for  a  small  machine,  using  air  at  a  pressure 
of  five  atmospheres  without  expansion. 

*Pernolet,  L'Air  Comprime,  pp.  549,  550. 

f  Revue  universelle  des  Mines,  2  S6rie,  Tome  vi. 


CHAPTER   XXI. 


REFRIGERATING   MACHINES. 

IN  the  discussion  of  heat-engines  it  appeared  that  the  sim- 
plest cycle  described  by  such  an  engine  is  that  for  Carnot's 

ideal  engine,  represented  by  Fig.  84. 
When  the  working  substance  in  the 
cylinder  P  is  a  gas  the  cycle  represented 
by  Fig.  85  is  composed  of  two  isother- 
mal lines,  AB  and  CD,  and  of  two  adi- 
abatic  lines,  BC  and  DA.  When  the 
working  substance  is  a  mixture  of  a 
liquid  and  its  vapor,  the  two  isothermal  lines  become  parallel 
to  the  axis  OV,  but  the  order  of  events  is  in  no  wise  altered. 

When  working  direct,  Carnot's  engine  takes  from  the  source 
of  heat  A  a  quantity  of  heat  Q,  changes  a  part  into  mechani- 
cal energy,  and  rejects  the  remainder  Ql  to  the  refrigerator  B. 
The  efficiency 

AW          -  T~  T 


FIG.  84. 


Q 


Q 


, 


increases  with  the  difference  of  temperatures  of  the  source  of 
heat  and  the  refrigerator. 

If  the  engine  be  reversed  so  that  it  describes  the  cycle  in 
the  order  ADCBA,  it  takes  heat  from  the  re- 
frigerator, adds  thereto  the  heat  equivalent  of 
the  work  of  the  cycle,  and  delivers  the  sum  to 
the  source  of  heat,  and  thus  becomes  a  refrig- 
erating machine.     It  is  apparent  that  in  this 
action  it  is  desirable  to  do  as  little  work  as  pos- 
sible on  the  working  substance,  and  that  this 
condition  is  fulfilled  by  making  the  difference  of  temperatures 
as  small  as  possible. 

434 


FIG.  85. 


REFRIGERATING  MACHINES.  435 

In  practice  it  is  found  convenient  to  supply  to  a  heat-engine 
at  each  stroke  a  quantity  of  the  working  substance  at  a  high 
temperature,  which  does  work  on  the  piston,  and  is  rejected  at 
a  lower  temperature.  Thus  the  steam-engine  takes  steam  from 
the  boiler  which  serves  as  a  source  of  heat,  and,  after  abstract- 
ing some  of  the  heat  in  the  form  of  work,  rejects  the  steam  to 
the  condenser  or  refrigerator.  In  like  manner  refrigerating 
machines  take  a  supply  of  the  working  substance  from  the  re- 
frigerator or  refrigerant,  do  work  upon  it,  and  deliver  it  at  a 
higher  temperature  to  a  receptacle  which  is  known  as  the  cooler 
or  condenser,  but  which  takes  the  place  of  the  source  of  heat 
or  boiler. 

Two  forms  of  refrigerating  machines  are  in  common  use — 
air -refrigerating  machines  and  compression -refrigerating  ma- 
chines using  a  saturated  vapor — such  as  the  ammonia-refriger- 
ating or  ice-machine. 

Air-refrigerating  Machine. — The  general  arrangement  of 
an  air-refrigerating  machine  is  shown  by  Fig.  86.  It  consists 
of  a  compression  cylinder  A,  an  expansion  cylinder  B  of  smaller 
size,  and  a  cooler  C.  It  is  commonly  used  to  keep  the  atmos- 
phere in  a  cold  storage-room  at  a  low  temperature,  and  has  cer- 
tain advantages  for  this  purpose,  especially  on  shipboard.  The 
air  from  the  storage-room  comes  to  the  compressor  at  or  about 
freezing-point,  is  compressed  to  two  or  three  atmospheres  and 
delivered  to  the  cooler,  which  has  the  same  form  as  a  surface  con- 
denser, with  cooling  water  entering  at  e  and  leaving  at  f.  From 
the  cooler  the  air,  usually  somewhat  warmer  than  the  atmos- 
phere, goes  to  the  expansion  cylinder^,  in  which  it  is  expanded 
nearly  to  the  pressure  of  the  air  and  cooled  to  a  low  temperature, 
and  then  delivered  to  the  storage-room.  The  inlet  valves 
a,  a  and  the  deli  very- valves  b,  b  of  the  compressor  are 
moved  by  the  air  itself ;  the  admission-valves  c,  c  and  the  ex- 
haust-valves d,  d  of  the  expansion  cylinder  are  like  those  of  a 
steam-engine,  and  must  be  moved  by  the  machine.  The  differ- 
ence between  the  work  done  on  the  air  in  the  compressor,  and 
that  done  by  the  air  in  the  expansion  cylinder,  together  with 


THERMODYNAMICS  OF  THE   STEAM-ENGINE. 


the  friction  work  of  the  whole  machine,  must  be  supplied  by  a 
steam-engine  or  other  motor. 

The  effect  of  clearance  in  the  compression  cylinder,  as  has 
been  seen  in  the  discussion  of  air-compressors,  is  to  increase 
the  size  required  for  a  certain  performance.  The  exhaust-valves 
of  the  expansion  cylinder  should  be  so  set  that  the  clearance 


FIG.  86. 


shall  be  filled  by  compression  with  air  at  nearly  if  not  quite  the 
admission  pressure,  and  the  cut-off  should  be  such  that  the  air 
shall  expand  down  to  the  back  pressure.  This  latter  is  always 
of  importance  for  the  efficient  action  of  the  machine,  but  if  the 
clearance  is  small  the  compression  is  of  less  moment. 

It  is  customary  to  provide  the  compression  cylinder  with  a 
water-jacket  to  prevent  overheating,  and  frequently  a  spray  of 
water  is  thrown  into  the  cylinder  to  reduce  the  heating  and  the 


I 

REFRIGERATING  MACHINES.  437 

work  of  compression.  Sometimes  the  cooler  C,  Fig.  86,  is  re- 
placed by  an  apparatus  resembling  a  steam-engine  jet  condenser, 
in  which  the  air  is  cooled  by  a  spray  of  water.  In  any  case  it  is 
essential  that  the  moisture  in  the  air,  as  well  as  the  water  injected, 
should  be  efficiently  removed  before  the  air  is  delivered  to  the 
expansion  cylinder,  otherwise  snow  will  form  in  that  cylinder 
and  interfere  with  the  action  of  the  machine.  Various  mechani- 
cal devices  have  been  used  to  collect  and  remove  water  from 
the  air,  but  air  may  be  saturated  with  moisture  after  it  has 
passed  such  a  device.  The  Bell-Coleman  Company  use  a  jet 
cooler  with  provision  for  collecting  and  withdrawing  water,  and 
then  pass  the  air  through  pipes  in  the  cold  room  on  the  way  to 
the  expansion  cylinder.  The  cold  room  is  maintained  at  a  tem- 
perature a  little  above  freezing-point,  so  that  the  moisture  in 
the  air  is  condensed  upon  the  sides  of  the  pipes  and  drains  back 
into  the  cooler.  The  same  machine,  as  made  by  Menck  and 
Hambrock,  is  provided  with  a  device  for  removing  moisture 
from  the  air,  that  is  shown  by  Fig.  87.  Air  from  the  cooler 
comes  in  by  the  pipe  a,  is  distributed  by  the  annular  perforated 
pipe  b,  and  passes  out  to  the  expansion  cylinder  by  the  pipe  c. 
The  chamber  E  is  surrounded  by  a  jacket  through  which  passes 
the  cold  air  on  the  way  from  the  expansion  cylinder  to  the 
cold  room.  Since  the  air  in  the  jacket  is  many  degrees  below 
freezing-point  the  walls  of  the  chamber  E  are  quickly  covered 
with  frost,  which  accumulates  till  a  considerable  thickness  is  at- 
tained ;  afterwards  the  moisture  condenses  and  runs  down  to 
the  bottom  of  the  chamber,  from  whence  it  is  withdrawn.  A 
coil  of  steam-pipe  dd  is  provided  for  thawing  ice  and  snow  that 
may  accumulate  at  the  bottom  of  the  chamber.  Since  the  same 
air  is  used  continuously,  being  taken  from  the  cold  room,  chilled 
and  returned,  the  effect  of  these  devices  is  to  remove  the  moist- 
ure from  the  air  in  the  cold  room  and  to  maintain  a  cold,  dry 
atmosphere  in  it,  which  is  well  adapted  to  preserving  all  kinds 
of  perishable  provisions. 

When  an  air-refrigerating  machine  is  used  as  described  the 
pressure  in  the  cold  room  is  necessarily  that  of  the  atmosphere, 
and  the  size  of  the  machine  is  large  as  compared  with  its  per- 


438 


THERMODYNAMICS  OF   THE  STEAM-ENGINE. 


formance.  The  performance  may  be  increased  by  running  the 
machine  on  a  closed  cycle  with  higher  pressures ;  for  example, 
the  cold  air  may  be  delivered  to  a  coil  of  pipe  in  a  non-freezing 
salt  solution,  from  which  the  air  abstracts  heat  through  the 
walls  of  the  pipe  and  then  passes  to  the  compressor  to  be  used 
over  again.  The  machine  may  then  be  used  to  produce  ice,  or 
the  brine  may  be  used  for  cooling  spaces  or  liquids.  A  machine 
has  been  used  for  producing  ice  on  a  small  scale,  without  cool- 
ing water,  on  the  reverse  of  this  principle :  that  is,  atmospheric 


FIG.  87. 


air  is  first  expanded  and  chilled  and  delivered  to  a  coil  of  pipe 
in  a  salt  solution,  then  the  air  is  drawn  from  this  coil,  after  ab- 
sorbing heat  from  the  brine,  compressed  to  atmospheric  pres- 
sure, and  expelled. 

Calculation  of  Air-refrigerating  Machine. — The  per- 
formance of  a  refrigerating  machine  may  be  stated  in  terms  of 
the  number  of  thermal  units  withdrawn  in  a  unit  of  time,  or 
in  terms  of  the  weight  of  ice  produced.  The  latent  heat  of 
fusion  of  ice  may  be  taken  to  be  80  calories  or  744  B.  T.  U. 

Let  the  pressure  at  which  the  air  enters  the  compression 
cylinder  be^ ,  that  at  which  it  leaves  be/a ;  let  the  pressure  at 


REFRIGERATING  MACHINES.  439 

cut-off  in  the  expanding  cylinder  be  /3  and  that  of  the  back 
pressure  in  the  same  be  pi ;  let  the  temperatures  corresponding 
to  these  pressures  be  tl ,  /2 ,  /3 ,  and  /4 ,  or  reckoned  from  the 
absolute  zero,  Tl ,  7, ,  Ts ,  and  T^ .  With  proper  valve-gear  and 
large,  short  pipes  communicating  with  the  cold  chamber,/, 
may  be  assumed  to  be  equal  to  p^ ,  and  equal  to  the  pressure  in 
that  chamber.  Also  tl  may  be  assumed  to  be  the  temperature 
maintained  in  the  cold  chamber,  and  /3  may  be  taken  to  be  the 
temperature  of  the  air  leaving  the  cooler.  With  a  good  cut- 
off mechanism  and  large  passages  /3  may  be  assumed  to  be 
nearly  the  same  as  that  of  the  air  supplied  to  the  expanding 
cylinder.  Owing  to  the  resistance  to  the  passage  of  the  air 
through  the  cooler  and  the  connecting  pipes  and  passages,  /8 
is  considerably  less  than  /2 . 

The  expansion  in  the  expanding  cylinder  may  be  assumed 
to  be  adiabatic,  so  that 


T. 


Were  the  compression  also  adiabatic,  the  temperature  /, 
could  be  determined  in  a  similar  manner  ;  but  the  air  is  usually 
cooled  during  compression,  and  contains  more  or  less  vapor,  so 
that  the  temperature  at  the  end  of  compression  cannot  be  de- 
termined from  the  pressure  alone,  even  though  the  equation  of 
the  expansion  curve  be  known. 

Let  the  air  passing  through  the  refrigerating  machine  per 
minute  be  M,  then  the  heat  withdrawn  from  the  cold  room  is 


(327) 


The  work  of  compressing  M  units  of  weight  of  air  from  the 
pressure/j  to  the  pressure/,  in  a  compressor  without  clearance  is 


Wc  =  J 

M     -JL 

"     -.,    .    (328) 


440  THERMODYNAMICS  OF   THE  STEAM-ENGINE. 

provided  that  the  compression  curve  can  be  represented  by  an 
exponential  equation.  The  work  will  be  the  same  for  a  com- 
pressor with  clearance  if  the  exponent  for  the  equation  to  the 
expansion  curve  is  the  same  as  that  for  the  compression  curve. 
If  the  compression  can  be  assumed  to  be  adiabatic, 


-*=-^    •  (3*9) 


for  in  such  case  we  have  the  equations 


Tt      /A\~ 

T>  ~  IA) 


The  work  done  by  the  air  in  the  expanding  cylinder  should 
be  calculated  in  the  manner  used  on  page  201  in  designing  a 
steam-engine,  or  on  page  325  for  finding  the  work  of  a  com- 
pressed-air engine.  If  the  expansion  and  compression  are 
both  complete,  then  the  work  done  by  M  units  of  weight  of  air  is 

Me 

w.  =  -j(tt-t)    gJS   •   (330) 

The  work  that  must  be  supplied  per  minute  is 
W=  Wc-  We, 

and  the  net  horse-power  required  is 

W 

H.  P.;. 


33000 

but  the  gross  horse-power  required  is  much  larger,  since  all  the 
frictional  resistances  must  be  overcome,  including  the  friction 
of  both  pistons.  The  proper  allowance  can  readily  be  deter- 
mined on  a  machine  with  a  steam-engine  coupled  direct,  by  in- 
dicating both  of  the  air-cylinders  and  the  steam-cylinder 
simultaneously. 


REFRIGERATING  MACHINES.  441 

The  heat  carried  away  by  the  cooling  water  is 

Q  =  Qg  +  AW.    ......    (331) 

If  compression  and  expansion  are  both  adiabatic,  then 
Q  =  Me  fa  -  *4  +  *,  -  A  -  *,  +  O  =  Me  fa  -  O-     (332) 


If  the  initial  and  final  temperatures  of  the  cooling  water  are 
ti  and  tk,  and  if  &  and  qk  are  the  corresponding  heats  of  the 
liquid,  then  the  weight  of  cooling  water  per  minute  is 


(333) 


A  good  supply  of  cooling  water  and  a  method  of  regulating 
it  should  be  provided,  so  that  an  approximate  calculation  may 
be  made  for  any  case,  under  the  assumption  of  adiabatic  com- 
pression and  expansion,  by  the  equation 


The  volume  of  the  compression  piston  displacement,  neglect- 
ing clearance,  is 


_^ 

°~'  ~> 


in  which  n  is  the  number  of  revolutions  per  minute,  and  /0  ,  z>0  , 
T0  are  the  pressure,  volume,  and  absolute  temperature,  at  at- 
mospheric pressure  and  at  freezing-point. 

If  it  be  assumed  that  /4  is  the  same  as  /t  ,  then  the  volume 
of  the  expanding  cylinder,  without  clearance,  may  be  assumed 
to  be 


(336) 


442  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

If  the  clearance  of  the  compressor  is  —  of  the  piston  dis- 
placement; then  the  volume  of  air  in  the  cylinder  when  the 
inlet-valve  opens  is 


m\A 

and  the  volume  calculated  by  equation  (335)  should  be  multi- 
plied by 


(337) 


If  the  expansion  and  compression  in  the  expanding  cylinder 
are  complete,  the  same  expression  may  be  used  to  allow  for 
clearance  in  that  cylinder,  making  n  equal  to  K.  To  allow  for 
loss  of  pressure  in  valves  and  passages  and  for  other  imperfec- 
tions, both  of  these  volumes  may  be  increased  by  an  amount 
to  be  determined  by  experiment.  In  practice  the  expansion 
is  seldom  carried  down  to  the  back  pressure  in  the  expanding 
cylinder,  nor  is  the  compression  complete,  and  the  volume  is 
smaller  than  that  given  by  equation  (336). 

The  temperature  Tt  may  be  controlled  by  the  cut-off  of  the 
expanding  cylinder,  and  thus  the  performance  of  the  machine 
may  be  varied.  As  the  cut-off  is  shortened  p^  is  increased  and 
7"4  diminished,  and  this  in  turn  makes  Ve  smaller  compared 
with  Vc. 

PROBLEM.  —  Required  the  dimensions  of  an  air-refrigerating 
machine  to  produce  an  effect  equal  to  the  melting  of  200  pounds 
of  ice  per  hour.  •  Let  the  pressure  in  the  cold  chamber  be  14.7 
pounds  and  the  temperature  32°  F.  Let  the  pressure  at  cut- 
off in  the  expanding  cylinder  be  29.4  pounds  by  the  indicator 
or  44.1  pounds  absolute.  Let  the  delivery  pressure  in  the  com- 
pressor be  39.4  pounds  by  the  indicator,  i.e.,  let  the  loss  of  pres- 
sure in  the  cooler  and  passages  be  10  pounds.  Let  the  initial 
and  final  temperatures  of  the  cooling  water  be  60°  and  80°  F., 


REFRIGERATING  MACHINES.  443 

and  the  temperature  of  the  air  from  the  cooler  90°  F.  Let  the 
machine  make  60  revolutions  per  minute. 

The  melting  of  200  pounds  of  ice  per  hour  is  equivalent  to 
28800  B.  T.  U.  per  hour,  or  480  B.  T.  U.  per  minute. 

Assuming  adiabatic  compression  and  expansion, 


=  492-7  ~      =  S^o  ;    /.  t,  =  -  100°.;  F.  ; 


"  =  4927         =  7I4'9  ;  •'•  '•  =  254°-2  F- 


The  air  used  per  minute  is  therefore 

480  -T-  (32  +  100.7)  X  0.2375  =  12.10  pounds. 

The  horse-power  of  the  compression  cylinder  with  adiabatic 
compression  is 

Wc         12.1  X  778  X  0.2375  x  (254.2  -  32) 

-  ~~- 


If  the  compression  curve  may  be  represented  by 

pv™  =  const., 
then  the  work  of  compression  will  be 


wc  =  12.1  x  144  x  14-7  x  12.4  x 


=  49230  foot-pounds, 


and  the  horse-power  is  therefore  14.0. 

The  horse-power  of  the  expanding  cylinder  is 

W.         12.1  X  778  X  0.2375  x  (32  +  100.7)  ~  T> 

-  =  9-0  H.  P. 


444  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  net  horse-power  required  is  therefore  6  H.  P.  or  5  H.  P., 
and  the  indicated  horse-power  of  the  steam-cylinder  may  be 
assumed  to  be  8  H.  P.  or  6f  H.  P.,  according  to  the  manner  of 
the  compression. 

The  volume  of  the  compressor-piston  displacement  without 
clearance  will  be 

12.1  X  12.4 

=  1.25  cubic  feet. 

The  volume  of  the  expanding  cylinder  under  the  same  con- 
dition is 

360 
1.25  x =  0.91  cubic  feet. 

If  the  clearance  of  the  compressor  be  assumed  to  be  O.O2, 
the  piston  displacement  should  be 

i 

!/$4.i\  1-2  ) 

i  +  0.02  -  -       —  0.02  [  =  1.4  cubic  feet. 
U4-7/  ) 

If  the  clearance  of  the  expanding  cylinder  be  assumed  to 
be  0.05,  the  piston  displacement  should  be 

_i 

5/44. 1X^4  ) 

i  +  0.05  ( — - J      —  0.05  >  =  0.96  cubic  foot. 

If,  further,  an  allowance  of  ten  per  cent  be  made  for  imper- 
fections, the  dimensions  may  be:  diameter,  compressor,  17 
inches;  diameter,  expanding  cylinder,  14  inches;  stroke,  12 
inches. 

Compression-refrigerating  Machine. — The  arrangement 
of  a  refrigerating  machine  using  a  volatile  liquid  and  its  vapor 
is  shown  by  Fig.  88.  The  essential  parts  are  the  compressor 
A,  the  condenser  B,  the  valve  D,  and  the  vaporizer  C.  The 
compressor  draws  in  vapor  at  a  low  pressure  and  temperature, 
compresses  it  and  delivers  it  to  the  condenser,  which  consists  of 
coils  of  pipe  surrounded  by  cooling  water  that  enters  at  e  and 


REFRIGERATING  MACHINES. 


445 


leaves  at  f.  The  vapor  is  condensed,  and  the  resulting  liquid 
gathers  in  a  reservoir  in  the  bottom,  from  whence  it  is  led  by 
a  small  pipe  having  a  regulating  valve  D  to  the  vaporizer  or 
refrigerator.  The  refrigerator  is  also  made  up  of  coils  of  pipe, 
and  is  immersed  in  a  non-freezing  solution  of  salt,  commonly 
chloride  of  calcium.  The  volatile  liquid  vaporizes  and  withdraws 
heat  from  the  surrounding  brine,  and  reduces  the  temperature 


DDOBQQ 


FIG.  88. 


below  the  freezing-point  of  water.  In  the  figure  the  machine 
is  represented  to  be  applied  to  ice-making,  the  water  being  in- 
troduced and  frozen  in  properly-shaped  moulds  of  thin  metal. 
When  the  machine  is  used  to  cool  a  room  the  vaporizer  may 
be  made  up  of  a  system  of  pipes  arranged  to  withdraw  heat 
from  the  air,  or  brine  may  be  cooled  and  circulated  through 
such  a  system  of  pipes.  When  brine  is  used  either  in  ice-mak- 
ing or  in  cooling,  a  positive  circulation  should  be  given  it  by  a 
pump  or  the  equivalent. 

In  Fig.  88  the  compressor  is  represented  as  single-acting, 
but  for  horizontal  machines  it  is  commonly  made  double-act- 


44-6  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

ing.  Frequently  the  compressor  has  two  single-acting  vertical 
cylinders  driven  by  a  horizontal  steam-engine  coupled  to  the 
shaft.  Such  compressors  sometimes  have  the  clearance  filled 
with  oil,  of  which  part  is  forced  through  the  delivery-valves 
and  allowed  to  flow  back  into  the  cylinder  during  the  inflow 
of  vapor.  In  any  case,  it  is  of  great  importance  that  the  clear- 
ance shall  be  reduced  to  the  smallest  amount  possible. 

To  make  the  cycle  of  the  machine  complete  the  liquid  from 
the  condenser  should  be  allowed  to  do  work  in  an  expansion 
cylinder  like  that  of  an  air-refrigerating  machine,  instead  of 
flowing  through  the  regulating  valve  D.  The  size  of  such  a 
cylinder  would  be  small,  and  the  work  recovered,  insignificant, 
so  that  none  of  the  machines  in  use  are  provided  with  such  an 
expansion  cylinder. 

Calculation  of  Compression  Machine. — Let  the  pressure 
in  the  condenser  be/!,  the  temperature  ^  ,  and  the  heat  of  the 
liquid  gl .  Let  the  pressure  in  the  vaporizer  or  refrigerator  be 
/, ,  the  temperature  /2 ,  and  the  total  heat  of  vaporization  A2. 
The  heat  withdrawn  from  the  refrigerant  to  change  one  unit  of 
weight  of  liquid  at  the  temperature  tl  into  saturated  vapor  at 
the  pressure/,  is 

*•  —  &  > 

so  that  the  heat  withdrawn  per  minute  by  a  machine  using  M 
units  of  weight  of  the  working  fluid  per  minute  is 

Ql^=M(\,-q>).        .'    .     .     .     .      (338) 

Even  though  the  compressor  cylinder  be  water-jacketed, 
the  walls  are  at  a  considerably  higher  temperature  than  the 
entering  vapor,  and  the  pressure  during  admission  is  a  little 
lower  than  that  in  the  vaporizer.  Also  most  of  the  vapors 
now  used  in  such  machines  are  superheated  by  adiabatic  com- 
pression. Therefore  it  is  probable  that  the  vapor  is  super- 
heated during  compression,  even  though  it  be  moist  as  it  leaves 
the  vaporizer.  For  an  approximate  calculation  it  may  be 
assumed  that  the  pressure  in  the  cylinder  during  admission  is 
/a ,  that  the  vapor  is  dry  and  saturated  at  the  beginning  of 


REFRIGERATING  MACHINES.  447 

compression,  and  that  it  is  compressed  adiabatically  and  super- 
heated during  the  entire  compression.  It  will  be  shown  that 
ammonia  and  sulphur  dioxide,  when  moderately  superheated, 
have  the  approximate  characteristic  equation 


......  (339) 

and  that  during  an  adiabatic  change  we  have  the  equation 

.......  (34o) 


During  the  expulsion  of  vapor  from  the  compressor  the 
pressure  in  the  cylinder  is  a  little  higher  than  in  the  condenser, 
but  it  may  be  assumed  to  be  the  same  for  our  approximate 
calculation.  The  temperature  of  the  vapor  leaving  the  com- 
pressor and  entering  the  condenser  may  consequently  be  cal- 
culated by  the  equation 


T, 


(340 


The  heat  that  must  be  withdrawn  by  the  cooling  water  is 
therefore 

(2  =  M\ejt.-t,)  +  r,|,      ....     (342) 

in  which  cp  is  the  specific  heat  of  the  superheatecj  vapor  at 
constant  pressure,  and  rl  is  the  heat  of  vaporization  at  the 
pressure  p^ . 

If  the  initial  and  final  temperatures  of  the  cooling  water  are 
/,-  and  tfc ,  and  if  £,.  and  <lk  are  the  corresponding  heats  of  the 
liquid  for  water,  then  the  weight  of  cooling  water  used  per 
minute  is 


44$  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

For  the  first  approximation  the  horse-power  of  the  com- 
pressor  may  be  calculated  by  the  expression 


778  ,, 

33000  %  ** 

The  power  thus  calculated  should  be  multiplied  by  a  factor 
to  be  found  by  experiment,  in  order  to  find  the  probable  indi- 
cated horse-power  of  the  compressor,  and  the  indicated  horse- 
power must  be  multiplied  by  another  factor  to  find  the  power 
required  to  drive  the  machine,  or  by  a  factor  to  find  the  indi- 
cated horse-power  of  a  steam-engine  coupled  to  the  shaft 
driving  the  compressor. 

If  the  actual  pressures  in  the  cylinder  of  the  compressor 
during  admission  and  delivery  are  p"  and  /',  if  the  specific 
volume  at  the  beginning  of  compression  is  v"  ,  and  if  the  com- 
pression and  expansion  curves  may  be  represented  by  the 
equation 


then  the  horse-power  of  the  compressor  may  be  found  by  the 
expression 

Mp"v" 
33000 


;£-,{()    -} 


If  the  vapor  at  the  beginning  of  compresssion  can  be 
assumed  to  be  dry  and  saturated,  then  the  volume  of  the 
piston  displacement  of  a  compressor  without  clearance,  and 
making  N  strokes  per  minute,  is 


,     ... 

(346) 


To  allow  for  clearance,  the  volume  thus  found  may  be  mul- 
tiplied by  the  factor 


REFRIGERAl^ING  MACHINES.  449 

in  which   --  is  the  clearance  expressed  as  a  fraction  of    the 

piston  displacement.  The.  volume  thus  found  is  further  to  be 
multiplied  by  a  factor  to  allow  for  inaccuracies  and  imperfec- 
tions. 

The  vapors  used  in  compression  machines  are  liable  to  be 
mingled  with  air  or  moisture,  and  in  such  case  the  performance 
of  the  machine  is  impaired.  To  allow  for  such  action  the  size 
and  power  of  the  machine  must  be  increased  in  practice  above 
those  given  by  calculation.  It  would  appear  that  proper  pre- 
cautions ought  to  be  taken  to  prevent  such  action  from  be- 
coming of  importance. 

PROBLEM.  —  Required  the  dimensions  of  an  ammonia-refrig- 
erating machine  to  produce  2000  pounds  of  ice  per  hour.  Let 
the  temperature  of  the  salt  solution  be  14°  F.  and  the  temper- 
ature in  the  condenser  86°  F.  ;  let  the  initial  and  final  temper- 
atures of  the  cooling  water  be  60°  and  80°  F.  Let  the  compres- 
sor be  double-acting,  and  let  it  make  60  revolutions  per  minute. 

The  pressures  corresponding  to  the  temperatures  14°  and 
86°  are  41.5  and  168.2  pounds,  absolute,  per  square  inch,  or 
26.8  and  153.8  pounds  by  the  gauge.  For  ammonia,  k  =  f  . 
Hence  by  equation  (341) 

Ts  =  (14  +  460.7) 


If  5  per  cent  be  allowed  for  ice  wasted  in  removing  it  from 
the  moulds,  and  for  other  losses,  the  capacity  of  the  machine 
per  minute  must  be 


/.  &  =  5040  =  M(\t  -  &)  =  M(SS4  -  59); 

5040 

.*.  M  =  —    -  —  10.2  pounds. 
495 


45°  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  heat  withdrawn  by  the  cooling  water  is 


Q  =  io.2{o.5o8(2i3  —  86)  +  497}  =  5727  B.  T.  U. 
The  cooling  water  required  per  minute  is,  consequently, 


The  horse-power  will  be,  approximately, 


33000 

_778x  10.2  Jo.5o8(2i3-  86)  +  556-297} 

33000  ~  77'*- 

The  horse-power  of  the  steam-cylinder  may  be  assumed 
to  be 

77.8  -T-  0.80  =  97.2. 

On  the  assumption  that  the  vapor  in  the  compressor  is  dry 
and  saturated  at  the  beginning  of  compression,  the  volume  of 
the  piston  displacement,  not  allowing  for  clearance,  is 

Mv^       10.2  x  7.05 
V=-=  3=  5.15  cub.c  feet. 


If  we  allow  10  per  cent  for  the  effect  of  clearance  and  im- 
perfect action,  then  the  volume  should  be  5.7  cubic  feet,  or 
about  2oJ  inches  in  diameter  by  30  inches  stroke. 

Fluids  Available.—  The  fluids  that  have  been  used  in 
compression-refrigerating  machines  are  ether,  sulphurous  acid, 
ammonia,  and  a  mixture  of  sulphurous  acid  and  carbonic  acid, 
known  as  Pictet's  fluid.  The  pressures  of  the  vapors  of  these 
fluids  at  several  temperatures,  and  also  the  pressure  of  the 


REFRIGERATING  MACHINES. 


451 


vapors  of  methylic  ether  and  carbonic  acid,  are  given  in  the 
following  table : 

PRESSURES  OF  VAPORS,  MM.  OF  MERCURY. 


Temperatures, 
degrees 
Centigrade. 

Ether. 

Sulphur 
Dioxide. 

Methyl- 
ether. 

Ammonia. 

Carbon 
Dioxide. 

Pictet's 
Fluid. 

—  -2O 

287."; 

576.  5 

866.1 

585 

—  20 
—  IO 
0 
10 
20 
30 
A.O 

68.9 
114.7 
184.4 
286.8 
432.8 
634-8 

QO7    O 

479-5 
762.5 
1165.1 
1719.6 
2462  .  i 
3431-8 
4670  2 

882.0 
1306.6 
1879.0 
2629.0 
3586.0 
4778.0 

I392-I 
2144.6 

3183.3 
4574-0 
6387-8 
8701.0 

TICQC    a 

15142 
20340 
26907 
34999 
44717 
56119 
69184 

745 
1018 

1391 
1938 
2584 
3382 

A'lA'l 

Ether  was  used  in  the  early  compression  machines,  but  at 
the  temperatures  maintained  in  the  refrigerator  the  pressure  is 
small  and  the  specific  volume  large,  so  that  the  machines,  like 
air-refrigerating  machines,  were  either  feeble  or  bulky.  More- 
over, air  was  liable  to  leak  into  the  machine  and  unduly  heat  the 
compressor  cylinder.  Sulphur  dioxide  has  been  used  success- 
fully, but  it  has  the  disadvantage  that  sulphuric  acid  may  be 
formed  by  the  leakage  of  moisture  into  the  machine,  in  which 
case  rapid  corrosion  occurs.  Ammonia  has  been  extensively  used 
in  the  more  recent  machines  with  good  results.  When  distilled 
from  an  aqueous  solution  it  is  liable  to  contain  considerable 
moisture.  As  is  shown  by  the  table,  Pictet's  fluid  has  a  pressure 
at  low  temperature  intermediate  between  the  pressures  of 
sulphur  dioxide  and  ammonia,  and  the  pressure  increases  slowly 
with  the  temperature. 

The  properties  of  saturated  vapor  of  ether  were  determined 
by  Regnault,  and  are  given  in  Chapter  VII.  For  the  other 
vapors  given  in  the  table  (except  Pictet's  fluid)  he  determined 
the  relations  of  the  temperature  and  pressure,  but  not  the 
total  heat  of  vaporization  nor  the  heat  of  the  liquid.  He  did, 
however,  determine  some  of  the  properties  of  these  substances 
in  the  gaseous  state,  or  more  properly,  in  the  state  of  super- 
heated vapors.  It  was  first  proposed  by  Ledoux  *  that  the 


*  Annales  des  Mines,  1878. 


45  2  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

properties  of  the  superheated  vapors  of  sulphur  dioxide  and 
ammonia  can  be  represented  by  equations  of  the  form  deduced 
by  Zeuner  for  superheated  steam,  and  that  the  application  of 
these  equations  to  the  saturated  vapors  as  the  limit  makes  it 
possible  to  calculate  the  properties  of  the  saturated  vapors 
approximately.  His  equations  do  not  fulfil  the  conditions 
given  by  equation  (166),  page  118,  and  do  not  represent  all  the 
properties  of  the  superheated  vapors,  given  by  Regnault ;  conse- 
quently new  equations  have  been  calculated  for  both  French 
and  English  units. 

Properties  of  Sulphur  Dioxide. — The  specific  heat  of 
gaseous  sulphur  dioxide  is  given  by  Regnault  *  as  0.15438,  and 
the  coefficient  of  dilatation  as  0.0x339028.  The  theoretical  spe- 
cific gravity  compared  with  air,  calculated  from  the  chemical 
composition,  is  given  by  Landolt  and  Bornsteinfas  2.21295. 
Gmelin  \  gives  the  following  experimental  determinations  :  by 
Thomson,  2.222  ;  by  Berzelius,  2.247.  The  figure  2.23  will  be 
assumed  in  this  work,  which  gives  for  the  specific  volume  at 
freezing-point  and  at  atmospheric  pressure 


cubic  metres.     The  corresponding  pressure  and  temperature 
are  10333,  and  273°-7  C. 

Now  the  coefficient  of  dilatation  is  the  ratio  of  the  increase 
of  volume  at  constant  pressure,  for  one  degree  increase  of  tem- 
perature, to  the  original  volume.  Writing  the  equation  (166), 


(347) 


*Memoires  de  1'Institut  de  France,  Tome  xxi.,  xxvi. 
f  Physikalische-chemische  Tabellen. 
\  Watt's  translation,  p.  280. 


REFRIGERATING  MACHINES.  453 

we  have  at  O°  C.  and  i°  C., 


>i  —  v0 


Substituting  the  known  values  and  solving  for  a,  we  obtain 
0.212;  but  the  equation  obtained  from  the  equation  (347)  with 
this  figure  does  not  agree  well  with  Regnault's  experiments  on 
the  compressibility  of  sulphur  dioxide.  If,  instead,  we  make 

a  =  0.22, 

then  by  equation  (347)  the  coefficient  of  dilatation  becomes 
0.00404,  and  it  will  be  shown  later  that  the  equation  deduced 
with  this  value  agrees  quite  well  with  the  experiments  on  com- 
pressibility. 

The  coefficient  of  T  in  equation  (347)  is  therefore 

0.15438  X  426.9  X  0.22  =  14.5, 
and  the  coefficient  of  pa  is 

14.5  x  273.7  -  10333  X  Q.347 
-  ==zz  -  -  =  48  nearly; 
10333 

so  that  the  equation  becomes 

pv=  14.5  ^-48/>'22  ......     (348) 

Regnault  found  for  the  pressures 

pi  =    697.83  mm.  of  mercury, 

/,  =  1341.58  " 


I  \ 

454  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

and  at  7°.7  C.  the  ratio 

Vft     <7I 

-  =  1.02088. 


Pfff. 

Reducing  the  given  pressures  to  kilograms  on  the  square 
inch,  and  the  temperature  to  the  absolute  scale,  and  applying  to 
equation  (347),  we  obtain  instead  of  the  experimental  value  for 
the  above  ratio  1.016. 

Regnault  gives  for  the  pressure  of  saturated  sulphur  diox- 
ide, in  mm.  of  mercury,  the  equation 

log  /  =  a  —  ban  —  cftn ; 

a  =  5.6663790 ; 
log  b  =  0.4792425  ; 
log  c  =  9.1659562  —  10; 
log  a  —  9.9972989  —  10 ; 
log  ft  =  9.98729002  —  10 ; 

n  =  t  +  28°  C. 

Applying  equations  (109)  and  (no),  page  80,  to  this  case, 


log  <x  =  9.9972989; 
log  ft  =  9.98729002  ; 
log  A  =  8.6352146; 
log  £=7.9945332; 
n  =  t  +  28°  C. 

The  specific  volume  of  saturated  sulphur  dioxide  may  be 
calculated. by.  inserting  in  equation  (347)  for  the  superheated 
vapor  the  pressures  calculated  by  aid  of  the  above  equation. 
The  results  at  several  temperatures  are  as  follows : 

/        -30°C.  o  +30°C. 

s         0.8292  0.2256  0.0825 


REFRIGERATING  MACHINES.  455 

Andre"  eff*  gives  for  the  specific  gravity  of  '  fluid  sulphur 
dioxide  14336;  consequently  the  specific  volume  of  the  liquid  is 

a  =  0.0007. 

The  value  of  r,  the  heat  of  vaporization,  may  now  be  calcu- 
lated at  the  given  temperatures  by  equation  (128), 


in  which  u  =  s  —  cr. 

The  results  are 

t          -3o°C.  o  +3Q°C. 

r  106.9  97.60  90.54 

Within  the  limits  of  error  of  our  method  of  calculation,  the 
value  of  r  may  be  found  by  the  equation 

r  —  98  —  0.27^. 

To  find  the  specific  heat  of  the  liquid,  we  may  use  equa- 
tion (180),  page  120, 

T   dp\  dr       r 


At  o°  C.  the  specific  heat  is  approximately 

c  =  0.4. 

In  English  units  we  have  for  superheated  sulphur  dioxide 
pv  =  26.4  T—  i84/022, 

the  pressures  being  in  pounds  on  the  square  foot,  the  volumes 
in  cubic  feet,  and  the  temperatures  in  Fahrenheit  degrees 
absolute. 

*Ann.  Chem.  Pharm.  1859. 


45°"  THERMODYNAMICS   OF    THE   STEAM-ENGINE. 

For  pressures  in  pounds  on  the  square  inch  at  temperatures 
on  the  Fahrenheit  scale, 

log/  —  a  —  ban  —  cfin\ 


log  b  =  0.4792425  ; 
log  c  —  9.1659562  —  10; 
loga  =  9.9984994—  10  ; 
log  /?  =  9.99293890  —  10  ; 
»  =  /+  i8°.4F. 

For  the  heat  of  vaporization 

r=  176  -0.270-32), 
and  for  the  specific  heat  of  the  liquid 

c  =  0.4. 

Properties  of  Ammonia.  —  The  specific  heat  of  gaseous 
ammonia,  determined  by  Regnault,  is  0.50836.  The  theoretical 
specific  gravity  compared  with  air,  calculated  from  the  chemical 
composition,  is  given  by  Landolt  and  Bornstein  as  0.58890. 
Gmelin  gives  the  following  experimental  determinations:  by 
Thomson,  0.5931  ;  by  Biot  and  Arago,  0.5967.  For  this  work 
the  figure  0.597  will  be  assumed,  which  gives  for  the  specific 
volume  at  freezing-point  and  at  atmospheric  pressure 


cubic  meters.  The  coefficient  of  dilatation  has  not  been  de- 
termined, and  consequently  cannot  be  used  to  determine  the 
value  of  a  in  equation  (347).  It,  however,  appears  that  very 
consistent  results  are  obtained  if  a  is  assumed  to  be  £,  as  for 
superheated  steam.  The  coefficient  of  T  then  becomes 

0.50836  x  426.9  x  i  =  54-3, 


REFRIGERATING  MACHINES.  457 

and  the  coefficient  of/*  is 

54.3  x  273.7-10333  x  1.30, 

-          i  -  —  I42  » 
10333 

so  that  the  equation  becomes 

/z/=  54-3^-  I42/*  ......    (349) 

The  coefficient  of  dilatation,  calculated  by  the  same  process 
as  that  used  in  determining  a  for  sulphur  dioxide,  is  0.00404, 
which  may  be  compared  with  that  for  sulphur  dioxide. 

Regnault  found  for  the  pressures 

pl  =    703.50  mm.  of  mercury, 
A  =  H35-3      " 
and  at  8°.i  C.  the  ratio 


while  equation  (349)  gives  under  the  same  conditions  1.0200. 
For  saturated  ammonia  Regnault  gives  the  equation 

log  /  =  a  —  ban  —  eft"  ; 

a=  11.5043330; 
log  b  =  0.8721769; 
log£  =  9-9777087—  10  ; 
log  a  =  9.9996014  —  10; 
log  ft  =  9-9939729  -  10  ; 


by  aid  of  which  the  pressures  in  mm.  of  mercury  may  be  calcu- 
lated for  temperatures  on  the  Centigrade  scale.  The  differen- 
tial coefficient  may  be  calculated  by  aid  of  the  equation 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

log  A  =  8.1635170  —  10  ; 
log  B  =  8.4822485  —  10  ; 
log  a  =  9.9996014  —  10; 

log  ft  =  9.9939729  —  I0  ; 

H  =  t  +  22°  C. 

The  specific  volume  of  saturated  ammonia  calculated  by 
equation  (339)  at  several  temperatures  are 

t       -  30°  C.  o  +  30°  C. 

s         0.9982  0.2961  0.1167 

Andr£eff  gives  for  the  specific  gravity  of  liquid  ammonia  at 
O°  C.,  0.6364,  so  that  the  specific  volume  of  the  liquid  is 

a  —  0.0016. 

The  values  of  r  at  the  several  given  temperatures,  calculated 
by  equation  (128),  are 

/         '-30°  C.  o  +30°C. 

r  325.7  300.15  277.5 

which  may  be  represented  by  the  equation  * 

r  =  300  —  o.8/. 

The  specific  heat  of  the  liquid,  calculated  by  aid  of  equa- 
tion (180),  is 

c  —  i.i. 

In  English  units  the  properties  of  superheated  or  gaseous 
ammonia  may  be  represented  by  the  equation 


in  which  the  pressures  are  taken  in  pounds  on  the  square  foot 
and  volumes  in  cubic  feet,  while  T  represents  the  absolute 
temperature  in  Fahrenheit  degrees. 


REFRIGERATING  MACHINES.  459 

The  pressure  in  pounds  on  the  square  inch  may  be  calcu- 
lated by  the  equation 

log  p  =  a  —  ban  —  cfin  ; 

a  =  9.790738o ; 
log  b  =  0.8721769  —  10 ; 
log  c  =  9-9777087  —  10  ; 
log  a  =  9.9997786  —  10 ; 
log  ft  =  9.9^66516  —  10 ; 
n  =  t  +  7°.6  F. 

The  heat  of  vaporization  may  be  calculated  by  the  equation 

r  =  540  -  o.8(*  -  32), 
and  the  specific  heat  of  the  liquid  is 

c  —  i.i. 

Pictet's  Fluid. — Attention  has  already  been  called  to  the 
mixture  of  sulphur  dioxide  and  carbon  dioxide  known  as  Pic- 
tet's fluid,  which  was  adopted  by  Pictet  for  use  in  his  refriger- 
ating machines  after  an  extended  investigation.  The  desirable 
properties  are  stated  by  him  to  be : 

1.  The  tension  of  the  vapor  should  be  greater  than  that  of 
sulphur  dioxide  and  less  than  that  of  ammonia.     The  boiling- 
point  under  atmospheric  pressure  should  be  about  —  2O°C. 

2.  The  tension   of  the  vapor   in  the  condenser  at  about 
-f-  30°  C.  should  be  between  7  and  8  atmospheres. 

3.  The  fluid  should  be  incombustible. 

4.  The  fluid  should  not  attack  metals. 

5.  The  fluid  should  have  such  a  chemical  composition  that 
changes  of  volatility  during  use  need  not  be  feared. 

6.  The  fluid  should  be  of  an  unctuous  nature,  so  that  oil  need 
not  be  used  on  the  piston  of  the  compressor. 

7.  The  fluid  should  be  inexpensive. 

An  investigation  of  the  properties  of  various  fluids  shows 
that  the  addition  of  oxygen  to  any  compound,  whether  it  en- 
tered in  solution  or  into  chemical  combination,  diminished  the 


460  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

volatility.  Thus  carbon  monoxide  boils  at  —  140°  C,  while 
carbon  dioxide  boils  at  —  75°  C. ;  sulphur  dioxide  boils  at 
—  10°  C.,  and  anhydrous  sulphurous  acid  boils  at  -|-  32°,  while 
the  hydrate  boils  at  -(-  326°  C.  Other  examples  are  given  by 
Pictet  showing  the  same  result.  As  a  result  of  experiments  on 
the  mixture  of  sulphur  dioxide  and  carbon  dioxide  he  gives 
the  following  table  of  boiling-points.  The  formulae  express 
the  proportion  of  the  elements  in  the  mixtures,  but  are  not  to 
be  taken  to  represent  chemical  compounds. 

Boiling-point.  Boiling-point. 

C400MS        -71°  CO.S,  -15° 

C1006,S        -54°  CO.S,  -12° 

C.O..S        -41°  C010S,  -90.5 

C,.OMS        -26°  CO12SS  —  8°.6 

CO.S  -  19°  COUS.  -  8° 

...  CO..S,  -7°.5 

The  mixture,  which  may  properly  be  expressed  by  the  for- 
mula CO2  +  SO2,  was  found  to  fulfil  all  the  seven  desirable 
properties,  and,  as  is  shown  by  the  table  on  page  (451),  the 
pressure  increases  less  rapidly  with  the  temperature  than  for 
simple  vapors,  so  that  while  the  pressure  at  —  30°  C.  is  double 
that  of  sulphur  dioxide,  the  pressure  at  -\-  30°  C.  is  a  little 
less  than  that  of. that  fluid.  This  remarkable  property  appears 
to  be  due  to  the  increased  solvent  action  of  the  two  fluids  on 
each  other  at  higher  pressures,  which  acts  to  diminish  the 
mechanical  work  of  compression  from  one  temperature  to 
another;  for  example,  in  the  compressor  of  a  refrigerating 
machine. 

Absorption  Refrigerating  Apparatus. — Fig.  89  gives 
an  ideal  diagram  of  a  continuous  absorption  refrigerating  ap- 
paratus. It  consists  of  the  following  essential  parts:  (i)  the 
generator  B,  containing  a  concentrated  solution  of  ammonia  in 
water,  from  which  the  ammonia  is  driven  by  heat ;  (2)  the  con- 
denser C,  consisting  of  a  coil  of  pipe  in  a  tank,  through  which 
cold  water  is  circulated  ;  (3)  the  valve  V,  for  regulating  the  pres- 
sures in  £7 and  in  /;  (4)  the  refrigerator/,  consisting  of  a  coil  of 


REFRIGERATING  MACHINES. 


461 


pipe  in  a  tank  containing  a  non-freezing  salt  solution  ;  (5)  the 
absorber  A,  containing  a  dilute  solution  of  ammonia,  in  which 
the  vapor  of  ammonia  is  absorbed ;  and  (6)  the  pump  P  for 
transferring  the  solution  from  the  bottom  of  A  to  the  top  of 
B ;  there  is  also  a  pipe  connecting  the  bottom  of  B  with  the  top 
of  A.  It  is  apparent  that  the  condenser  and  refrigerator  or 
vaporizer  correspond  to  the  parts  B  and  C  of  Fig.  88,  and 
that  the  absorber  and  generator  take  the  place  of  the  com- 


FIG.  89. 

pressor.  The  pipes  connecting  A  and  B  are  arranged  to  take 
the  most  concentrated  solution  from  A  to  B,  and  to  return 
the  solution  from  which  the  ammonia  has  been  driven,  from  B 
to  A.  In  practice  the  generator  B  is  placed  over  a  furnace,  by 
which  heat  is  applied  to  drive  off  the  ammonia.  Also,  arrange- 
ments are  made  for  transferring  heat  from  the  hot  liquid  flow- 
ing from  B  to  A  to  the  cold  liquid  flowing  from  A  to  B.  As 
the  ammonia  is  distilled  from  water  in  B  the  vapor  driven  off 
contains  some  moisture,  which  causes  an  unavoidable  loss  of 
efficiency. 

The  earliest  absorption  apparatus,  made  by  Carre,  consisted 
of  a  cylindrical  receptacle  containing  a  solution  of  ammonia, 
and  acting  alternately  as  generator  and  absorber,  in  open  com- 
munication through  a  pipe  with  a  vessel  of  double  conical 
form,  acting  alternately  as  condenser  and  refrigerator.  In  use, 
the  generator  was  placed  on  a  furnace  and  the  condenser  in  a 
tank  of  cold  water,  and  the  ammonia  driven  off  from  the  solu- 
tion condensed  between  the  inner  and  outer  conical  surfaces  of 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

the  condenser.  When  a  sufficient  amount  of  liquid  ammonia 
had  collected,  the  vessel  containing  the  solution  was  transferred 
from  the  furnace  to  the  cold-water  tank,  and  became  thereby 
changed  into  the  absorber.  The  condenser  at  the  same  time 
became  the  vaporizer  or  refrigerator,  and  after  receiving  a 
mould  containing  water  to  be  frozen,  was  securely  wrapped 
with  non-conducting  material.  Apparatus  of  this  kind  is  only 
fitted  for  work  on  a  small  scale,  and  is  inefficient. 

An  adaptation  of  Carre's  apparatus  has  been  used  in  re- 
frigerator cars  for  carrying  perishable  freight.  In  the  car  are 
placed  two  receptacles — one  containing  liquid  ammonia,  which 
maintains  a  low  temperature  by  vaporization  ;  and  the  other 
containing  water,  to  absorb  the  ammonia  as  it  is  formed.  At 
the  end  of  the  route,  or  when  necessary,  the  receptacles  are  re- 
charged— one  with  liquid  ammonia  and  the  other  with  fresh 
water.  The  ammonia  in  the  rejected  solution  is  regained  by 
distillation. 

Vacuum  Refrigerating  Apparatus. — A  form  of  absorption 
apparatus  uses  water  for  the  volatile  liquid  and  concentrated 
sulphuric  acid  for  the  absorbent.  From  the  fact  that  vapor  of 
water  at  freezing-point  has  a  very  low  tension,  such  apparatus 
are  called  vacuum  apparatus. 

The  first  apparatus  of  this  kind  was  designed  for  freezing 
water  in  carafes,  and  consisted  of  a  good  air-pump,  and  a  re- 
ceptacle containing  oil  of  vitriol.  The  carafe,  well  wrapped  in 
non-conductor,  was  attached  to  a  pipe  leading  to  the  sulphuric 
acid  receptacle,  the  pump  was  worked  till  a  good  vacuum  was 
produced,  and  the  acid  was  stirred  to  present  fresh  acid  to  the 
vapor  which  rapidly  streamed  from  the  water  at  the  low  pres- 
sure produced.  The  vaporization  of  about  one  sixth  of  the 
weight  of  the  water  was  found  to  be  sufficient  to  freeze  the 
remainder. 

An  ideal  sketch  of  a  continuous  vacuum  apparatus  is  shown 
by  Fig.  90.  At  B  is  an  air-pump  capable  of  producing  a 
vacuum  of  one  or  two  mm.  of  mercury,  in  the  chamber  AC. 
At  H  there  is  a  tank  of  concentrated  sulphuric  acid,  from  which 
a  spray  is  delivered  at  J.  The  acid  absorbs  the  vapor  found 


REFRIGERATING  MACHINES. 


463 


in  the  chamber  at  the  low  pressure  existing  there,  gathers  in 
the  tank/,  and  flows  out  through  the  pipe  K,  which  is  of  suf- 
ficient length  to  deliver  the  acid  against  atmospheric  pressure 


FIG.  90. 

in  the  tank  L.  The  dilute  acid  is  reconcentrated  and  returned 
to  the  tank  H.  At  G  is  a  pipe  supplying  fresh  water,  which 
passes  through  the  water-injector  s,  and  throws  a  jet  of  salt 
solution  into  the  chamber  at  A.  The  finely  divided  jet  loses 
fresh  water  by  vaporization,  is  chilled,  and  gathers  in  the  bot- 
tom of  the  chamber.  The  salt  solution  flows  through  the  pipe 
F  in  the  cold  chamber  EE,  taking  up  heat  on  the  way,  and  is 
again  thrown  into  the  chamber  with  a  fresh  supply  of  water 
from  the  pipe  G.  At  N  and  N  are  screens  to  prevent  splash- 
ing of  water  into  the  upper  part  of  the  chamber. 

Schroter's  Tests  of  Refrigerating  Machines. — Professor 
M.  Schroter*  made  a  number  of  tests  on  various  forms  of  re- 
frigerating machines,  in  the  years  1885-1887,  to  determine  the 
efficiency  of  such  apparatus  in  practice.  From  his  report  the 
following  tests  have  been  taken  : 

*  Untersuchungen  an  Kaltemaschinen. 


464 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


Test  of  a  Bell-Coleman  Machine. — An  air-refrigerating 
machine,  constructed  under  the  Bell-Coleman  patents,  was  tested 
at  an  abattoir  in  Hamburg,  where  it  was  used  to  maintain  a 
low  temperature  in  a  storage-room.  The  machine  is  horizontal, 
and  has  the  pistons  for  the  expansion  and  compression  cylinders 
on  one  piston-rod,  the  expansion  cylinder  being  nearer  the 
crank.  Power  is  furnished  by  a  steam-engine  acting  on  a  crank 
at  the  other  end  of  the  main  shaft,  and  at  right  angles  to 
the  crank  driving  the  air-pistons.  Both  the  steam-cylinder  and 
the  expansion  cylinder  have  distribution  slide-valves,  with  inde_ 
pendent  cut-off  valves.  The  main  dimensions  are  given  in  the 
following  table : 

DIMENSIONS    BELL-COLEMAN  MACHINE. 


Steam 
Cylinder. 

Compression 
Cylinder. 

Expansion 
Cylinder. 

Head 
end. 

Crank 
end. 

Head 
end. 

Crank 
end. 

Head 
end. 

Crank 
end. 

Diameter  of  piston,  cm  

85? 

0.605 

5-9 

6'l 

0.605 

5-8 

71 
9.0 

0.605 
1.4 

6?8 
0.605 
1.4 

53 
9.0 
0.605 
8.9 

53 
9.0 
0.605 
8.9 

'*        "  piston-rod  cm 

Stroke   m 

Clearance,  per  cent  of  piston  displacement. 

Water  is  sprayed  into  the  compression  cylinder,  and  the  air 
is  further  cooled  by  passing  through  an  apparatus  resembling 
a  steam-engine  jet  condenser,  after  which  it  is  dried  by  passing 
it  through  a  system  of  pipes  in  the  cold  room  before  it  passes 
to  the  expansion  cylinder. 

In  the  tests  indicators  were  attached  to  each  end  of  the 
several  cylinders,  and  the  temperature  of  the  air  was  taken  at 
entrance  to  and  exit  from  each  of  the  air-cylinders.  Speci- 
mens of  the  indicator-diagrams  from  the  air-cylinders  show, 
for  the  compressor,  a  slight  reduction  of  pressure  during  ad- 
mission and  some  irregularity  during  expulsion,  and  for  the 
expansion  cylinder,  a  little  wire-drawing  at  cut-off,  and  a  good 
expansion  and  compression,  though  neither  are  complete.  No 
attempt  was  made  to  measure  the  amount  and  temperatures  of 
the  cooling  water. 

The  data  and  results  of  the  tests  and  the  calculations  are 
given  in  Table  XXXV. 


REFRIGERATING  MACHINES. 


465 


TABLE   XXXV. 

TESTS  ON  BELL-COLEMAN  MACHINE. 


Number  of  Test                     

I. 

II. 

in 

6 

i  6^ 

61  2 

*    y 

Temperatures  of  air,  degrees  Centigrade: 

IQ.7 

26  8 

16  6 

Mean  effective  pressure,  kgs.  per  sq.  cm.: 

crank  end  

2.23Q 

i  861 

i  870 

i  860 

i  82=; 

6 

Expansion  cylinder  *  head  end      

I    c8n 

i  626 

Indicated  horse-power: 

85    12 

82  Q=C 

gc    7i 

128    85 

6 

Mean  pressure  during  expulsion  from  compression  cylinder,.kgs. 
Mean  pressure  during  admission  to  expansion  cylinder,  kgs.  .  .  . 
Difference  

3-35 

2.82 
0.53 

3-25 
2.83 

0.42 

3-40 

,.84 

Calculation  from  compression  diagram: 

Absolute  pressure  at  opening  of  admission-valve,  kg.  : 

o  78^? 

o  788 

Crank  end            

* 

Volume  at  admission,  per  cent  of  piston  displacement: 

6  i=; 

8  =;o 

8  41 

Weight  of  air  discharged  per  stroke,  kg.: 

Weight  of  air  discharged  per  revolution,  kg  

O    54.8 

Calculation  from  expansion  diagram: 
Absolute  pressure  at  release,  kgs.: 

Crank  end     

**« 

I   46 

Absolute  pressure  at  compression,  kgs.: 

Volume  at  release,  per  cent  of  p.  d.: 
Head  end             

104  8 

Volume  at  compression,  per  cent  of  p.  d.: 
Head  end                                        

16  5 

16  6 

IQ  8 

Air  used  per  stroke,  kg.: 

O   2^8 

Crank  end  

Air  used  per  revolution 

o  488 

o  487 

Difference  of  weights,  calculated   by  compression  and  expan- 
sion diagrams,  kg  

In  per  cent  of  the  former 

ii  6 

Mean  weight  of  air  per  revolution,  kg  

Elevation  of  temperature  at  constant  pressure,  degrees  Centi- 
grade 

66  7 

64.  =; 

66  i 

Heat  withdrawn  per  hour,  calories  

371 

067 

Tests  of  Compression  Machines.— In  Table  XXXVI  are 
given  the  data  and  results  of  tests  on  three  refrigerating  ma- 
chines on  the  Linde  system  using  ammonia,  and  of  a  machine 
on  Pictet's  system  using  Pictet's  fluid.  The  tests  on  machines 
used  for  making  ice  were  necessarily  of  considerable  length, 


466 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


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468  THERMODYNAMICS   OF   THE    STEAM-ENGINE. 

but  the  tests  on  machines  used  for  cooling  liquids  would  be  of 
shorter  duration. 

The  cooling  water  when  measured  was  gauged  on  a  weir  or 
through  an  orifice.  In  the  tests  3  to  6  on  a  machine  used  for 
cooling  fresh  water  the  heat  withdrawn  was  determined  by 
taking  the  temperatures  of  the  water  cooled,  and  by  gauging 
the  flow  through  an  orifice,  for  which  the  coefficient  of  flow 
was  determined  by  direct  experiment.  The  heat  withdrawn  in 
the  tests  7  and  8  was  estimated  by  comparison  with  the  tests  3 
to  6.  The  net  production  of  ice  in  the  tests  I  and  2  was  deter- 
mined directly;  and  in  the  test  2  the  loss  from  melting  during 
the  removal  from  the  moulds  was  found  by  direct  experiment 
to  be  8.45  per  cent.  By  comparison  with  this,  the  loss  by 
melting  in  the  first  test  was  estimated  to  be  7.7  per  cent.  The 
gross  production  of  ice  in  the  refrigerator  was  calculated  from 
the  net  production  by  aid  of  these  figures.  In  the  tests  9  to 
12  on  the  Pictet  machine  the  gross  production  was  determined 
from  the  weight  of  water  supplied,  and  the  net  production 
from  the  weight  of  ice  withdrawn. 

A  separate  experiment  on  the  machine  used  for  cooling 
brine  gave  the  following  results  for  the  distribution  of  power: 

Total  horse-power, 57.1 

Power  expended  on  compressor,     .......     19.5 

"  "  "    centrifugal  pump, 9.8 

"  "  "   water-pump, 3.6 

The  centrifugal  pump  was  used  for  circulating  the  brine 
through  a  system  of  pipes  used  for  cooling  a  cellar  of  a  brew- 
ery. The  water-pump  supplied  cooling  water  to  the  condenser 
and  for  other  purposes. 

A  similar  test  on  the  Pictet  machine  gave  : 

Power  of  engine  alone, 7.9  H.  P. 

"        "  engine  and  intermediate  gear,     .     .     16.6    "    " 
"        "   engine,  gear,  and  pump,    ....     20.0     "    " 

From  the  above  data  the  following  table  was  arranged  for 
the  several  tests  on  this  machine : 


REFRIGERATING  MACHINES. 
INDICATED  AND  EFFECTIVE  WORK. 


469 


Number  of  Test. 

9 

10 

11 

12 

19.9 
7-9 
77.1 
91.2 
0.84 

20.0 

8.0 

80.  1 

94-5 
0.85 

20.  o 

7-9 
84.6 

I* 

19.9 

7-9 
94-4 
109.8 
0.85 

65-  9(?) 
52.0 
o.79(?) 

68.9 
61.7 
0.89 

iii 

0.90 

83-2 
75-° 
0.90 

Mechanical  efficiency  of  compressor  

Test  of  an  Absorption  Machine. — The  principal  data  and 
the  results  of  a  test  made  by  Professor  J.  E.  Denton,*  on  an 
absorption  ammonia-refrigerating  machine,  are  given  in  Table 
XXXVII.  The  machine  is  applied  to  chill  a  room  of  about 
400,000  cubic  feet  capacity  at  a  pork-packing  establishment  at 
New  Haven,  Conn.  In  connection  with  this  test  the  specific 
heat  of  the  brine,  which  served  as  a  carrier  of  heat  from  the 
cold  room  to  the  ammonia,  was  determined  by  direct  experi- 
ment. The  brine  chilled  and  the  cooling  water  used  were 
measured  with  meters,  which  were  afterwards  tested  under  the 
conditions  of  the  experiment. 

TABLE  XXXVII. 

TEST  OF  AN  ABSORPTION  MACHINE. — SEVEN  DAYS'  CONTINUOUS  TEST, 
SEPT.  11-18,  1888. 


j 

ICQ   77 

Average    pressures 

Steam                   . 

J.7    7O 

above  atmospheres 

Cooler  

2  a   60 

in  Ibs.  per  sq.  in. 

27   j. 

Atmosphere  in  vicinity  of  machine  

80 

Generator                            . 

2720 

(  Inlet.  . 

21.  2O5 

Bnne    {outlet 

16.16 

(  Inlet 

54i 

Condenser  \  ^t^y/."  .'.".y^y  "  [  ]  ] 

80 

Average     tempera- 

( Inlet 

80 

tures  in    Fahren-^ 

Absorber]  ^Y'  ;••••;;;;;;••;;;•-;; 

in 

heit  degrees. 

(  Upper  outlet  to  generator  

212 

Heater  \  Lower       "     "  absorber 

I78 

(  Inlet  from  absorber  

132 

272° 

Water  returned  to  main  boilers  from  steam 
coil   

26O 

*  Trans.  Am.  Soc.  Mech.  Eng.,  vol.  x.,  May,  1889. 


470 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


Average    range    of  (  Condenser 

temperatures-?  Absorber. 31 

Fahr.  degrees.        (Brine I 5.13 

Brine  circulated  per  j  Cubic  feet 1,633.7 

hour.                         |  Pounds ....  119,260 

Specific  heat  of  brine 0.800 

Cooling  capacity  of  machine  in  tons  of  ice  per  day  of  24  hours. .  40.67 
Steam  consumption    per   hour,  to   volatilize   ammonia,  and   to 

operate  ammonia  pump Ibs.  1,986 

Eliminated  •!  Per  pound  of  brme 4  - 104 

'd  \  Total  per  hour 481,260 

Of  refrigerating  effect  per  pound  of  steam 

consumption 243 

P    .         ,  j  At  condenser,  per  hour 918,000 

British    thermal  ,jec  'a  |  At  absorber  "         1,116,000 

units.  "^  f  On  entering  genera- 

Per  pound  of  steam  J  n  toli  coiJ J'2O3 

I  On   leaving  genera- 

[      tor  coil 271 

Consumed  by  generator  per  Ib.  of  steam 

condensed 932 

Condensing  water  per  hour,  in  Ibs 36,000 

Equivalent  ice   production   per  pound  of  coal,  if  one   pound  of 

coal  evaporates  ten  pounds  of  steam  at  boiler 17.1 

Calories,  refrigerating  effect  per  kilogramme  of  steam  consumed.  135 

(  Condensing  coil 870 

i 

f                                  Dia.  steam  cyl 9 

Ammonia  pump  •     "     ammonia  cyl 3f 

Sizes,  in  inches,   of]                                   Stroke 10 

duplex  pumps.       j                                   Dia.  steam  cyl 9^ 

I  Brine              "          "    brine      "  8 

t                                  Stroke 10 

Total  revolutions  j  Ammonia  pump,  one 22 

per  minute.             (  Brine  pump,  two 70 

Effective  stroke  of  pumps,  part  of  full  stroke. 0. 


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